mathgenerator.geometry
1import random 2import math 3from math import cos, sin, pi 4 5 6def angle_btw_vectors(max_elt_amt=20): 7 r"""Angle between 2 vectors 8 9 | Ex. Problem | Ex. Solution | 10 | --- | --- | 11 | angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is: | $0.81$ radians | 12 """ 13 s = 0 14 v1 = [ 15 round(random.uniform(0, 1000), 2) 16 for i in range(random.randint(2, max_elt_amt)) 17 ] 18 v2 = [round(random.uniform(0, 1000), 2) for i in v1] 19 for i in range(len(v1)): 20 s += v1[i] * v2[i] 21 22 mags = math.sqrt(sum([i**2 23 for i in v1])) * math.sqrt(sum([i**2 for i in v2])) 24 solution = '' 25 ans = 0 26 try: 27 ans = round(math.acos(s / mags), 2) 28 solution = f"${ans}$ radians" 29 except ValueError: 30 print('angleBtwVectorsFunc has some issues with math module, line 16') 31 solution = 'NaN' 32 ans = 'NaN' 33 # would return the answer in radians 34 problem = f"angle between the vectors ${v1}$ and ${v2}$ is:" 35 return problem, solution 36 37 38def angle_regular_polygon(min_val=3, max_val=20): 39 r"""Angle of a Regular Polygon 40 41 | Ex. Problem | Ex. Solution | 42 | --- | --- | 43 | Find the angle of a regular polygon with $8$ sides | $135.0$ | 44 """ 45 sideNum = random.randint(min_val, max_val) 46 problem = f"Find the angle of a regular polygon with ${sideNum}$ sides" 47 48 exteriorAngle = round((360 / sideNum), 2) 49 solution = f'${180 - exteriorAngle}$' 50 51 return problem, solution 52 53 54def arc_length(max_radius=49, max_angle=359): 55 r"""Arc length of Angle 56 57 | Ex. Problem | Ex. Solution | 58 | --- | --- | 59 | Given radius, $44$ and angle, $184$. Find the arc length of the angle. | Arc length of the angle $= 141.30186$ | 60 """ 61 radius = random.randint(1, max_radius) 62 angle = random.randint(1, max_angle) 63 angle_arc_length = float((angle / 360) * 2 * math.pi * radius) 64 formatted_float = "{:.5f}".format(angle_arc_length) 65 66 problem = f"Given radius, ${radius}$ and angle, ${angle}$. Find the arc length of the angle." 67 solution = f"Arc length of the angle $= {formatted_float}$" 68 return problem, solution 69 70 71def area_of_circle(max_radius=100): 72 r"""Area of Circle 73 74 | Ex. Problem | Ex. Solution | 75 | --- | --- | 76 | Area of circle with radius $29=$ | $2642.08$ | 77 """ 78 r = random.randint(0, max_radius) 79 area = round(pi * r * r, 2) 80 81 problem = f'Area of circle with radius ${r}=$' 82 return problem, f'${area}$' 83 84 85def area_of_circle_given_center_and_point(max_coordinate=10, max_radius=10): 86 r"""Area of Circle given center and a point on circle 87 88 | Ex. Problem | Ex. Solution | 89 | --- | --- | 90 | Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is | $113.1$ | 91 """ 92 r = random.randint(0, max_radius) 93 center_x = random.randint(-max_coordinate, max_coordinate) 94 center_y = random.randint(-max_coordinate, max_coordinate) 95 96 angle = random.choice([0, pi // 6, pi // 2, pi, pi + pi // 6, 3 * pi // 2]) 97 98 point_x = center_x + round(r * cos(angle), 2) 99 point_y = center_y + round(r * sin(angle), 2) 100 101 area = round(pi * r * r, 2) 102 103 problem = f"Area of circle with center $({center_x},{center_y})$ and passing through $({point_x}, {point_y})$ is" 104 return problem, f'${area}$' 105 106 107def area_of_trapezoid(max_len=20): 108 r"""Area of Trapezoid 109 110 | Ex. Problem | Ex. Solution | 111 | --- | --- | 112 | Area of trapezoid with height $12$ and base lengths: $3, 7, = $ | $60$ | 113 """ 114 a = random.randint(1, max_len) 115 b = random.randint(1, max_len) 116 h = random.randint(1, max_len) 117 118 area = (a + b) * h / 2 119 120 problem = f"Area of trapezoid with height ${h}$ and base lengths: ${a}, {b}, = $" 121 solution = f'${round(area, 2)}$' 122 return problem, solution 123 124 125def area_of_triangle(max_a=20, max_b=20): 126 r"""Area of Triangle 127 128 | Ex. Problem | Ex. Solution | 129 | --- | --- | 130 | Area of triangle with side lengths: $8, 1, 8 = $ | $3.99$ | 131 """ 132 a = random.randint(1, max_a) 133 b = random.randint(1, max_b) 134 c = random.randint(abs(b - a) + 1, abs(a + b) - 1) 135 136 s = (a + b + c) / 2 137 area = (s * (s - a) * (s - b) * (s - c))**0.5 138 139 problem = f"Area of triangle with side lengths: ${a}, {b}, {c} = $" 140 solution = f'${round(area, 2)}$' 141 return problem, solution 142 143 144# Handles degrees in quadrant one 145def basic_trigonometry(angles=[0, 30, 45, 60, 90], 146 functions=["sin", "cos", "tan"]): 147 r"""Trigonometric Values 148 149 | Ex. Problem | Ex. Solution | 150 | --- | --- | 151 | $\sin(30) = $ | $\frac{1}{2}$ | 152 """ 153 angle = random.choice(angles) 154 function = random.choice(functions) 155 156 problem = rf"$\{function}({angle}) = $" 157 158 expression = 'math.' + function + '(math.radians(angle))' 159 result_fraction_map = { 160 0.0: "0", 161 0.5: r"\frac{1}{2}", 162 0.71: r"\frac{1}{\sqrt{2}}", 163 0.87: r"\frac{\sqrt{3}}{2}", 164 1.0: "1", 165 0.58: r"\frac{1}{\sqrt{3}}", 166 1.73: r"\sqrt{3}", 167 } 168 169 solution = result_fraction_map[round( 170 eval(expression), 171 2)] if round(eval(expression), 172 2) <= 99999 else r"\infty" # for handling the ∞ condition 173 174 return problem, f'${solution}$' 175 176 177def circumference(max_radius=100): 178 r"""Circumference of Circle 179 180 | Ex. Problem | Ex. Solution | 181 | --- | --- | 182 | Circumference of circle with radius $56 = $ | $351.86$ | 183 """ 184 r = random.randint(0, max_radius) 185 circumference = round(2 * math.pi * r, 2) 186 187 problem = f"Circumference of circle with radius ${r} = $" 188 return problem, f'${circumference}$' 189 190 191def complementary_and_supplementary_angle(max_supp=180, max_comp=90): 192 r"""Complementary and Supplementary Angle 193 194 | Ex. Problem | Ex. Solution | 195 | --- | --- | 196 | The complementary angle of $15 =$ | $75$ | 197 """ 198 angleType = random.choice(["supplementary", "complementary"]) 199 200 if angleType == "supplementary": 201 angle = random.randint(1, max_supp) 202 angleAns = 180 - angle 203 else: 204 angle = random.randint(1, max_comp) 205 angleAns = 90 - angle 206 207 problem = f"The {angleType} angle of ${angle} =$" 208 solution = f'${angleAns}$' 209 return problem, solution 210 211 212def curved_surface_area_cylinder(max_radius=49, max_height=99): 213 r"""Curved surface area of a cylinder 214 215 | Ex. Problem | Ex. Solution | 216 | --- | --- | 217 | What is the curved surface area of a cylinder of radius, $44$ and height, $92$? | $25434.33$ | 218 """ 219 r = random.randint(1, max_radius) 220 h = random.randint(1, max_height) 221 csa = float(2 * math.pi * r * h) 222 formatted_float = round(csa, 2) # "{:.5f}".format(csa) 223 224 problem = f"What is the curved surface area of a cylinder of radius, ${r}$ and height, ${h}$?" 225 solution = f"${formatted_float}$" 226 return problem, solution 227 228 229def degree_to_rad(max_deg=360): 230 r"""Degrees to Radians 231 232 | Ex. Problem | Ex. Solution | 233 | --- | --- | 234 | Angle $113$ degrees in radians is: | $1.97$ | 235 """ 236 a = random.randint(0, max_deg) 237 b = (math.pi * a) / 180 238 b = round(b, 2) 239 240 problem = f"Angle ${a}$ degrees in radians is: " 241 solution = f'${b}$' 242 return problem, solution 243 244 245def equation_of_line_from_two_points(max_coordinate=20, min_coordinate=-20): 246 r"""Equation of line from two points 247 248 | Ex. Problem | Ex. Solution | 249 | --- | --- | 250 | What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form? | $y = 4x -43$ | 251 """ 252 x1 = random.randint(min_coordinate, max_coordinate) 253 x2 = random.randint(min_coordinate, max_coordinate) 254 255 y1 = random.randint(min_coordinate, max_coordinate) 256 y2 = random.randint(min_coordinate, max_coordinate) 257 258 coeff_y = (x2 - x1) 259 coeff_x = (y2 - y1) 260 constant = y2 * coeff_y - x2 * coeff_x 261 262 gcd = math.gcd(abs(coeff_x), abs(coeff_y)) 263 264 if gcd != 1: 265 if coeff_y > 0: 266 coeff_y //= gcd 267 if coeff_x > 0: 268 coeff_x //= gcd 269 if constant > 0: 270 constant //= gcd 271 if coeff_y < 0: 272 coeff_y = -(-coeff_y // gcd) 273 if coeff_x < 0: 274 coeff_x = -(-coeff_x // gcd) 275 if constant < 0: 276 constant = -(-constant // gcd) 277 if coeff_y < 0: 278 coeff_y = -(coeff_y) 279 coeff_x = -(coeff_x) 280 constant = -(constant) 281 if coeff_x in [1, -1]: 282 if coeff_x == 1: 283 coeff_x = '' 284 else: 285 coeff_x = '-' 286 if coeff_y in [1, -1]: 287 if coeff_y == 1: 288 coeff_y = '' 289 else: 290 coeff_y = '-' 291 292 problem = f"What is the equation of the line between points $({x1},{y1})$ and $({x2},{y2})$ in slope-intercept form?" 293 if coeff_x == 0: 294 solution = str(coeff_y) + "y = " + str(constant) 295 elif coeff_y == 0: 296 solution = str(coeff_x) + "x = " + str(-constant) 297 else: 298 if constant > 0: 299 solution = str(coeff_y) + "y = " + str(coeff_x) + \ 300 "x + " + str(constant) 301 else: 302 solution = str(coeff_y) + "y = " + \ 303 str(coeff_x) + "x " + str(constant) 304 return problem, f'${solution}$' 305 306 307def fourth_angle_of_quadrilateral(max_angle=180): 308 r"""Fourth Angle of Quadrilateral 309 310 | Ex. Problem | Ex. Solution | 311 | --- | --- | 312 | Fourth angle of quadrilateral with angles $162 , 43, 78 =$ | $77$ | 313 """ 314 angle1 = random.randint(1, max_angle) 315 angle2 = random.randint(1, 240 - angle1) 316 angle3 = random.randint(1, 340 - (angle1 + angle2)) 317 318 sum_ = angle1 + angle2 + angle3 319 angle4 = 360 - sum_ 320 321 problem = f"Fourth angle of quadrilateral with angles ${angle1} , {angle2}, {angle3} =$" 322 solution = f'${angle4}$' 323 return problem, solution 324 325 326def perimeter_of_polygons(max_sides=12, max_length=120): 327 r"""Perimeter of Polygons 328 329 | Ex. Problem | Ex. Solution | 330 | --- | --- | 331 | The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is: | $319$ | 332 """ 333 size_of_sides = random.randint(3, max_sides) 334 sides = [random.randint(1, max_length) for _ in range(size_of_sides)] 335 336 problem = f"The perimeter of a ${size_of_sides}$ sided polygon with lengths of ${', '.join(map(str, sides))}$cm is: " 337 solution = sum(sides) 338 339 return problem, f'${solution}$' 340 341 342def pythagorean_theorem(max_length=20): 343 """Pythagorean Theorem 344 345 | Ex. Problem | Ex. Solution | 346 | --- | --- | 347 | What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$? | $13.45$ | 348 """ 349 a = random.randint(1, max_length) 350 b = random.randint(1, max_length) 351 c = round((a**2 + b**2)**0.5, 2) 352 353 problem = f"What is the hypotenuse of a right triangle given the other two sides have lengths ${a}$ and ${b}$?" 354 solution = f"${c}$" 355 return problem, solution 356 357 358def radian_to_deg(max_rad=6.28): 359 """Radians to Degrees""" 360 a = random.randint(0, int(max_rad * 100)) / 100 361 b = round((180 * a) / math.pi, 2) 362 363 problem = f"Angle ${a}$ radians in degrees is: " 364 solution = f'${b}$' 365 return problem, solution 366 367 368def sector_area(max_radius=49, max_angle=359): 369 """Area of a Sector 370 371 | Ex. Problem | Ex. Solution | 372 | --- | --- | 373 | What is the area of a sector with radius $42$ and angle $83$ degrees? | $1277.69$ | 374 """ 375 r = random.randint(1, max_radius) 376 a = random.randint(1, max_angle) 377 secArea = float((a / 360) * math.pi * r * r) 378 formatted_float = round(secArea, 2) 379 380 problem = f"What is the area of a sector with radius ${r}$ and angle ${a}$ degrees?" 381 solution = f"${formatted_float}$" 382 return problem, solution 383 384 385def sum_of_polygon_angles(max_sides=12): 386 """Sum of Angles of Polygon 387 388 | Ex. Problem | Ex. Solution | 389 | --- | --- | 390 | What is the sum of interior angles of a polygon with $8$ sides? | $1080$ | 391 """ 392 side_count = random.randint(3, max_sides) 393 sum = (side_count - 2) * 180 394 395 problem = f"What is the sum of interior angles of a polygon with ${side_count}$ sides?" 396 return problem, f'${sum}$' 397 398 399def surface_area_cone(max_radius=20, max_height=50, unit='m'): 400 """Surface area of a cone 401 402 | Ex. Problem | Ex. Solution | 403 | --- | --- | 404 | Surface area of cone with height $= 26m$ and radius $= 6m$ is | $616 m^2$ | 405 """ 406 a = random.randint(1, max_height) 407 b = random.randint(1, max_radius) 408 409 slopingHeight = math.sqrt(a**2 + b**2) 410 ans = int(math.pi * b * slopingHeight + math.pi * b * b) 411 412 problem = f"Surface area of cone with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 413 solution = f"${ans} {unit}^2$" 414 return problem, solution 415 416 417def surface_area_cube(max_side=20, unit='m'): 418 """Surface area of a cube 419 420 | Ex. Problem | Ex. Solution | 421 | --- | --- | 422 | Surface area of cube with side $= 6m$ is | $216 m^2$ | 423 """ 424 a = random.randint(1, max_side) 425 ans = 6 * (a**2) 426 427 problem = f"Surface area of cube with side $= {a}{unit}$ is" 428 solution = f"${ans} {unit}^2$" 429 return problem, solution 430 431 432def surface_area_cuboid(max_side=20, unit='m'): 433 """Surface area of a cuboid 434 435 | Ex. Problem | Ex. Solution | 436 | --- | --- | 437 | Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is | $936 m^2$ | 438 """ 439 a = random.randint(1, max_side) 440 b = random.randint(1, max_side) 441 c = random.randint(1, max_side) 442 ans = 2 * (a * b + b * c + c * a) 443 444 problem = f"Surface area of cuboid with sides of lengths: ${a}{unit}, {b}{unit}, {c}{unit}$ is" 445 solution = f"${ans} {unit}^2$" 446 return problem, solution 447 448 449def surface_area_cylinder(max_radius=20, max_height=50, unit='m'): 450 """Surface area of a cylinder 451 452 | Ex. Problem | Ex. Solution | 453 | --- | --- | 454 | Surface area of cylinder with height $= 26m$ and radius $= 15m$ is | $3864 m^2$ | 455 """ 456 a = random.randint(1, max_height) 457 b = random.randint(1, max_radius) 458 ans = int(2 * math.pi * a * b + 2 * math.pi * b * b) 459 460 problem = f"Surface area of cylinder with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 461 solution = f"${ans} {unit}^2$" 462 return problem, solution 463 464 465def surface_area_pyramid(unit='m'): 466 """Surface area of a pyramid 467 468 | Ex. Problem | Ex. Solution | 469 | --- | --- | 470 | Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is | $2400 m^2$ | 471 """ 472 # List of Pythagorean triplets 473 _PYTHAGOREAN = [(3, 4, 5), (6, 8, 10), (9, 12, 15), (12, 16, 20), 474 (15, 20, 25), (5, 12, 13), (10, 24, 26), (7, 24, 25)] 475 476 # Generate first triplet 477 height, half_width, _ = random.sample( 478 random.choice(_PYTHAGOREAN), 3) 479 480 # Calculate the first triangle height 481 triangle_height_1 = math.sqrt((half_width)**2 + height**2) 482 483 # Generate second triplet 484 second_triplet = random.choice([i for i in _PYTHAGOREAN if height in i]) 485 half_length, _ = random.sample( 486 tuple(i for i in second_triplet if i != height), 2) 487 488 # Calculate the second triangle height 489 triangle_height_2 = math.sqrt((half_length)**2 + height**2) 490 491 # Calculate triangles area 492 triangle_1 = half_length * triangle_height_1 493 triangle_2 = half_width * triangle_height_2 494 495 # Calculate base area 496 base = 4 * half_width * half_length 497 ans = base + 2 * triangle_1 + 2 * triangle_2 498 499 problem = f"Surface area of pyramid with base length $= {2*half_length}{unit}$, base width $= {2*half_width}{unit}$, and height $= {height}{unit}$ is" 500 solution = f"${ans} {unit}^2$" 501 return problem, solution 502 503 504def surface_area_sphere(max_side=20, unit='m'): 505 """Surface area of a sphere 506 507 | Ex. Problem | Ex. Solution | 508 | --- | --- | 509 | Surface area of a sphere with radius $= 8m$ is | $804.25 m^2$ | 510 """ 511 r = random.randint(1, max_side) 512 ans = round(4 * math.pi * r * r, 2) 513 514 problem = f"Surface area of a sphere with radius $= {r}{unit}$ is" 515 solution = f"${ans} {unit}^2$" 516 return problem, solution 517 518 519def third_angle_of_triangle(max_angle=89): 520 """Third Angle of Triangle 521 522 | Ex. Problem | Ex. Solution | 523 | --- | --- | 524 | Third angle of triangle with angles $10$ and $22 =$ | $148$ | 525 """ 526 angle1 = random.randint(1, max_angle) 527 angle2 = random.randint(1, max_angle) 528 angle3 = 180 - (angle1 + angle2) 529 530 problem = f"Third angle of triangle with angles ${angle1}$ and ${angle2} = $" 531 return problem, f'${angle3}$' 532 533 534def valid_triangle(max_side_length=50): 535 """Valid Triangle 536 537 | Ex. Problem | Ex. Solution | 538 | --- | --- | 539 | Does triangel with sides $10, 31$ and $14$ exist? | No | 540 """ 541 sideA = random.randint(1, max_side_length) 542 sideB = random.randint(1, max_side_length) 543 sideC = random.randint(1, max_side_length) 544 545 sideSums = [sideA + sideB, sideB + sideC, sideC + sideA] 546 sides = [sideC, sideA, sideB] 547 548 exists = True & (sides[0] < sideSums[0]) & (sides[1] < sideSums[1]) & ( 549 sides[2] < sideSums[2]) 550 551 problem = f"Does triangle with sides ${sideA}, {sideB}$ and ${sideC}$ exist?" 552 solution = "Yes" if exists else "No" 553 return problem, f'${solution}$' 554 555 556def volume_cone(max_radius=20, max_height=50, unit='m'): 557 """Volume of a cone 558 559 | Ex. Problem | Ex. Solution | 560 | --- | --- | 561 | Volume of cone with height $= 44m$ and radius $= 11m$ is | $5575 m^3$ | 562 """ 563 a = random.randint(1, max_height) 564 b = random.randint(1, max_radius) 565 ans = int(math.pi * b * b * a * (1 / 3)) 566 567 problem = f"Volume of cone with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 568 solution = f"${ans} {unit}^3$" 569 return problem, solution 570 571 572def volume_cube(max_side=20, unit='m'): 573 """Volume of a cube 574 575 | Ex. Problem | Ex. Solution | 576 | --- | --- | 577 | Volume of a cube with a side length of $19m$ is | $6859 m^3$ | 578 """ 579 a = random.randint(1, max_side) 580 ans = a**3 581 582 problem = f"Volume of cube with a side length of ${a}{unit}$ is" 583 solution = f"${ans} {unit}^3$" 584 return problem, solution 585 586 587def volume_cuboid(max_side=20, unit='m'): 588 """Volume of a cuboid 589 590 | Ex. Problem | Ex. Solution | 591 | --- | --- | 592 | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ | 593 """ 594 a = random.randint(1, max_side) 595 b = random.randint(1, max_side) 596 c = random.randint(1, max_side) 597 ans = a * b * c 598 599 problem = f"Volume of cuboid with sides = ${a}{unit}, {b}{unit}, {c}{unit}$ is" 600 solution = f"${ans} {unit}^3$" 601 return problem, solution 602 603 604def volume_cylinder(max_radius=20, max_height=50, unit='m'): 605 """Volume of a cylinder 606 607 | Ex. Problem | Ex. Solution | 608 | --- | --- | 609 | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ | 610 """ 611 a = random.randint(1, max_height) 612 b = random.randint(1, max_radius) 613 ans = int(math.pi * b * b * a) 614 615 problem = f"Volume of cylinder with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 616 solution = f"${ans} {unit}^3$" 617 return problem, solution 618 619 620def volume_cone_frustum(max_r1=20, max_r2=20, max_height=50, unit='m'): 621 """Volume of the frustum of a cone 622 623 | Ex. Problem | Ex. Solution | 624 | --- | --- | 625 | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ | 626 """ 627 h = random.randint(1, max_height) 628 r1 = random.randint(1, max_r1) 629 r2 = random.randint(1, max_r2) 630 ans = round(((math.pi * h) * (r1**2 + r2**2 + r1 * r2)) / 3, 2) 631 632 problem = f"Volume of frustum with height $= {h}{unit}$ and $r1 = {r1}{unit}$ is and $r2 = {r2}{unit}$ is " 633 solution = f"${ans} {unit}^3$" 634 return problem, solution 635 636 637def volume_hemisphere(max_radius=100): 638 """Volume of a hemisphere 639 640 | Ex. Problem | Ex. Solution | 641 | --- | --- | 642 | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ | 643 """ 644 r = random.randint(1, max_radius) 645 ans = round((2 * math.pi / 3) * r**3, 2) 646 647 problem = f"Volume of hemisphere with radius ${r} m =$ " 648 solution = f"${ans} m^3$" 649 return problem, solution 650 651 652def volume_pyramid(max_length=20, max_width=20, max_height=50, unit='m'): 653 """Volume of a pyramid 654 655 | Ex. Problem | Ex. Solution | 656 | --- | --- | 657 | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ | 658 """ 659 length = random.randint(1, max_length) 660 width = random.randint(1, max_width) 661 height = random.randint(1, max_height) 662 663 ans = round((length * width * height) / 3, 2) 664 665 problem = f"Volume of pyramid with base length $= {length} {unit}$, base width $= {width} {unit}$ and height $= {height} {unit}$ is" 666 solution = f"${ans} {unit}^3$" 667 return problem, solution 668 669 670def volume_sphere(max_radius=100): 671 """Volume of a sphere 672 673 | Ex. Problem | Ex. Solution | 674 | --- | --- | 675 | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ | 676 """ 677 r = random.randint(1, max_radius) 678 ans = round((4 * math.pi / 3) * r**3, 2) 679 680 problem = f"Volume of sphere with radius ${r} m = $" 681 solution = f"${ans} m^3$" 682 return problem, solution
def
angle_btw_vectors(max_elt_amt=20):
7def angle_btw_vectors(max_elt_amt=20): 8 r"""Angle between 2 vectors 9 10 | Ex. Problem | Ex. Solution | 11 | --- | --- | 12 | angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is: | $0.81$ radians | 13 """ 14 s = 0 15 v1 = [ 16 round(random.uniform(0, 1000), 2) 17 for i in range(random.randint(2, max_elt_amt)) 18 ] 19 v2 = [round(random.uniform(0, 1000), 2) for i in v1] 20 for i in range(len(v1)): 21 s += v1[i] * v2[i] 22 23 mags = math.sqrt(sum([i**2 24 for i in v1])) * math.sqrt(sum([i**2 for i in v2])) 25 solution = '' 26 ans = 0 27 try: 28 ans = round(math.acos(s / mags), 2) 29 solution = f"${ans}$ radians" 30 except ValueError: 31 print('angleBtwVectorsFunc has some issues with math module, line 16') 32 solution = 'NaN' 33 ans = 'NaN' 34 # would return the answer in radians 35 problem = f"angle between the vectors ${v1}$ and ${v2}$ is:" 36 return problem, solution
Angle between 2 vectors
| Ex. Problem | Ex. Solution |
|---|---|
| angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is: | $0.81$ radians |
def
angle_regular_polygon(min_val=3, max_val=20):
39def angle_regular_polygon(min_val=3, max_val=20): 40 r"""Angle of a Regular Polygon 41 42 | Ex. Problem | Ex. Solution | 43 | --- | --- | 44 | Find the angle of a regular polygon with $8$ sides | $135.0$ | 45 """ 46 sideNum = random.randint(min_val, max_val) 47 problem = f"Find the angle of a regular polygon with ${sideNum}$ sides" 48 49 exteriorAngle = round((360 / sideNum), 2) 50 solution = f'${180 - exteriorAngle}$' 51 52 return problem, solution
Angle of a Regular Polygon
| Ex. Problem | Ex. Solution |
|---|---|
| Find the angle of a regular polygon with $8$ sides | $135.0$ |
def
arc_length(max_radius=49, max_angle=359):
55def arc_length(max_radius=49, max_angle=359): 56 r"""Arc length of Angle 57 58 | Ex. Problem | Ex. Solution | 59 | --- | --- | 60 | Given radius, $44$ and angle, $184$. Find the arc length of the angle. | Arc length of the angle $= 141.30186$ | 61 """ 62 radius = random.randint(1, max_radius) 63 angle = random.randint(1, max_angle) 64 angle_arc_length = float((angle / 360) * 2 * math.pi * radius) 65 formatted_float = "{:.5f}".format(angle_arc_length) 66 67 problem = f"Given radius, ${radius}$ and angle, ${angle}$. Find the arc length of the angle." 68 solution = f"Arc length of the angle $= {formatted_float}$" 69 return problem, solution
Arc length of Angle
| Ex. Problem | Ex. Solution |
|---|---|
| Given radius, $44$ and angle, $184$. Find the arc length of the angle. | Arc length of the angle $= 141.30186$ |
def
area_of_circle(max_radius=100):
72def area_of_circle(max_radius=100): 73 r"""Area of Circle 74 75 | Ex. Problem | Ex. Solution | 76 | --- | --- | 77 | Area of circle with radius $29=$ | $2642.08$ | 78 """ 79 r = random.randint(0, max_radius) 80 area = round(pi * r * r, 2) 81 82 problem = f'Area of circle with radius ${r}=$' 83 return problem, f'${area}$'
Area of Circle
| Ex. Problem | Ex. Solution |
|---|---|
| Area of circle with radius $29=$ | $2642.08$ |
def
area_of_circle_given_center_and_point(max_coordinate=10, max_radius=10):
86def area_of_circle_given_center_and_point(max_coordinate=10, max_radius=10): 87 r"""Area of Circle given center and a point on circle 88 89 | Ex. Problem | Ex. Solution | 90 | --- | --- | 91 | Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is | $113.1$ | 92 """ 93 r = random.randint(0, max_radius) 94 center_x = random.randint(-max_coordinate, max_coordinate) 95 center_y = random.randint(-max_coordinate, max_coordinate) 96 97 angle = random.choice([0, pi // 6, pi // 2, pi, pi + pi // 6, 3 * pi // 2]) 98 99 point_x = center_x + round(r * cos(angle), 2) 100 point_y = center_y + round(r * sin(angle), 2) 101 102 area = round(pi * r * r, 2) 103 104 problem = f"Area of circle with center $({center_x},{center_y})$ and passing through $({point_x}, {point_y})$ is" 105 return problem, f'${area}$'
Area of Circle given center and a point on circle
| Ex. Problem | Ex. Solution |
|---|---|
| Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is | $113.1$ |
def
area_of_trapezoid(max_len=20):
108def area_of_trapezoid(max_len=20): 109 r"""Area of Trapezoid 110 111 | Ex. Problem | Ex. Solution | 112 | --- | --- | 113 | Area of trapezoid with height $12$ and base lengths: $3, 7, = $ | $60$ | 114 """ 115 a = random.randint(1, max_len) 116 b = random.randint(1, max_len) 117 h = random.randint(1, max_len) 118 119 area = (a + b) * h / 2 120 121 problem = f"Area of trapezoid with height ${h}$ and base lengths: ${a}, {b}, = $" 122 solution = f'${round(area, 2)}$' 123 return problem, solution
Area of Trapezoid
| Ex. Problem | Ex. Solution |
|---|---|
| Area of trapezoid with height $12$ and base lengths: $3, 7, = $ | $60$ |
def
area_of_triangle(max_a=20, max_b=20):
126def area_of_triangle(max_a=20, max_b=20): 127 r"""Area of Triangle 128 129 | Ex. Problem | Ex. Solution | 130 | --- | --- | 131 | Area of triangle with side lengths: $8, 1, 8 = $ | $3.99$ | 132 """ 133 a = random.randint(1, max_a) 134 b = random.randint(1, max_b) 135 c = random.randint(abs(b - a) + 1, abs(a + b) - 1) 136 137 s = (a + b + c) / 2 138 area = (s * (s - a) * (s - b) * (s - c))**0.5 139 140 problem = f"Area of triangle with side lengths: ${a}, {b}, {c} = $" 141 solution = f'${round(area, 2)}$' 142 return problem, solution
Area of Triangle
| Ex. Problem | Ex. Solution |
|---|---|
| Area of triangle with side lengths: $8, 1, 8 = $ | $3.99$ |
def
basic_trigonometry(angles=[0, 30, 45, 60, 90], functions=['sin', 'cos', 'tan']):
146def basic_trigonometry(angles=[0, 30, 45, 60, 90], 147 functions=["sin", "cos", "tan"]): 148 r"""Trigonometric Values 149 150 | Ex. Problem | Ex. Solution | 151 | --- | --- | 152 | $\sin(30) = $ | $\frac{1}{2}$ | 153 """ 154 angle = random.choice(angles) 155 function = random.choice(functions) 156 157 problem = rf"$\{function}({angle}) = $" 158 159 expression = 'math.' + function + '(math.radians(angle))' 160 result_fraction_map = { 161 0.0: "0", 162 0.5: r"\frac{1}{2}", 163 0.71: r"\frac{1}{\sqrt{2}}", 164 0.87: r"\frac{\sqrt{3}}{2}", 165 1.0: "1", 166 0.58: r"\frac{1}{\sqrt{3}}", 167 1.73: r"\sqrt{3}", 168 } 169 170 solution = result_fraction_map[round( 171 eval(expression), 172 2)] if round(eval(expression), 173 2) <= 99999 else r"\infty" # for handling the ∞ condition 174 175 return problem, f'${solution}$'
Trigonometric Values
| Ex. Problem | Ex. Solution |
|---|---|
| $\sin(30) = $ | $\frac{1}{2}$ |
def
circumference(max_radius=100):
178def circumference(max_radius=100): 179 r"""Circumference of Circle 180 181 | Ex. Problem | Ex. Solution | 182 | --- | --- | 183 | Circumference of circle with radius $56 = $ | $351.86$ | 184 """ 185 r = random.randint(0, max_radius) 186 circumference = round(2 * math.pi * r, 2) 187 188 problem = f"Circumference of circle with radius ${r} = $" 189 return problem, f'${circumference}$'
Circumference of Circle
| Ex. Problem | Ex. Solution |
|---|---|
| Circumference of circle with radius $56 = $ | $351.86$ |
def
complementary_and_supplementary_angle(max_supp=180, max_comp=90):
192def complementary_and_supplementary_angle(max_supp=180, max_comp=90): 193 r"""Complementary and Supplementary Angle 194 195 | Ex. Problem | Ex. Solution | 196 | --- | --- | 197 | The complementary angle of $15 =$ | $75$ | 198 """ 199 angleType = random.choice(["supplementary", "complementary"]) 200 201 if angleType == "supplementary": 202 angle = random.randint(1, max_supp) 203 angleAns = 180 - angle 204 else: 205 angle = random.randint(1, max_comp) 206 angleAns = 90 - angle 207 208 problem = f"The {angleType} angle of ${angle} =$" 209 solution = f'${angleAns}$' 210 return problem, solution
Complementary and Supplementary Angle
| Ex. Problem | Ex. Solution |
|---|---|
| The complementary angle of $15 =$ | $75$ |
def
curved_surface_area_cylinder(max_radius=49, max_height=99):
213def curved_surface_area_cylinder(max_radius=49, max_height=99): 214 r"""Curved surface area of a cylinder 215 216 | Ex. Problem | Ex. Solution | 217 | --- | --- | 218 | What is the curved surface area of a cylinder of radius, $44$ and height, $92$? | $25434.33$ | 219 """ 220 r = random.randint(1, max_radius) 221 h = random.randint(1, max_height) 222 csa = float(2 * math.pi * r * h) 223 formatted_float = round(csa, 2) # "{:.5f}".format(csa) 224 225 problem = f"What is the curved surface area of a cylinder of radius, ${r}$ and height, ${h}$?" 226 solution = f"${formatted_float}$" 227 return problem, solution
Curved surface area of a cylinder
| Ex. Problem | Ex. Solution |
|---|---|
| What is the curved surface area of a cylinder of radius, $44$ and height, $92$? | $25434.33$ |
def
degree_to_rad(max_deg=360):
230def degree_to_rad(max_deg=360): 231 r"""Degrees to Radians 232 233 | Ex. Problem | Ex. Solution | 234 | --- | --- | 235 | Angle $113$ degrees in radians is: | $1.97$ | 236 """ 237 a = random.randint(0, max_deg) 238 b = (math.pi * a) / 180 239 b = round(b, 2) 240 241 problem = f"Angle ${a}$ degrees in radians is: " 242 solution = f'${b}$' 243 return problem, solution
Degrees to Radians
| Ex. Problem | Ex. Solution |
|---|---|
| Angle $113$ degrees in radians is: | $1.97$ |
def
equation_of_line_from_two_points(max_coordinate=20, min_coordinate=-20):
246def equation_of_line_from_two_points(max_coordinate=20, min_coordinate=-20): 247 r"""Equation of line from two points 248 249 | Ex. Problem | Ex. Solution | 250 | --- | --- | 251 | What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form? | $y = 4x -43$ | 252 """ 253 x1 = random.randint(min_coordinate, max_coordinate) 254 x2 = random.randint(min_coordinate, max_coordinate) 255 256 y1 = random.randint(min_coordinate, max_coordinate) 257 y2 = random.randint(min_coordinate, max_coordinate) 258 259 coeff_y = (x2 - x1) 260 coeff_x = (y2 - y1) 261 constant = y2 * coeff_y - x2 * coeff_x 262 263 gcd = math.gcd(abs(coeff_x), abs(coeff_y)) 264 265 if gcd != 1: 266 if coeff_y > 0: 267 coeff_y //= gcd 268 if coeff_x > 0: 269 coeff_x //= gcd 270 if constant > 0: 271 constant //= gcd 272 if coeff_y < 0: 273 coeff_y = -(-coeff_y // gcd) 274 if coeff_x < 0: 275 coeff_x = -(-coeff_x // gcd) 276 if constant < 0: 277 constant = -(-constant // gcd) 278 if coeff_y < 0: 279 coeff_y = -(coeff_y) 280 coeff_x = -(coeff_x) 281 constant = -(constant) 282 if coeff_x in [1, -1]: 283 if coeff_x == 1: 284 coeff_x = '' 285 else: 286 coeff_x = '-' 287 if coeff_y in [1, -1]: 288 if coeff_y == 1: 289 coeff_y = '' 290 else: 291 coeff_y = '-' 292 293 problem = f"What is the equation of the line between points $({x1},{y1})$ and $({x2},{y2})$ in slope-intercept form?" 294 if coeff_x == 0: 295 solution = str(coeff_y) + "y = " + str(constant) 296 elif coeff_y == 0: 297 solution = str(coeff_x) + "x = " + str(-constant) 298 else: 299 if constant > 0: 300 solution = str(coeff_y) + "y = " + str(coeff_x) + \ 301 "x + " + str(constant) 302 else: 303 solution = str(coeff_y) + "y = " + \ 304 str(coeff_x) + "x " + str(constant) 305 return problem, f'${solution}$'
Equation of line from two points
| Ex. Problem | Ex. Solution |
|---|---|
| What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form? | $y = 4x -43$ |
def
fourth_angle_of_quadrilateral(max_angle=180):
308def fourth_angle_of_quadrilateral(max_angle=180): 309 r"""Fourth Angle of Quadrilateral 310 311 | Ex. Problem | Ex. Solution | 312 | --- | --- | 313 | Fourth angle of quadrilateral with angles $162 , 43, 78 =$ | $77$ | 314 """ 315 angle1 = random.randint(1, max_angle) 316 angle2 = random.randint(1, 240 - angle1) 317 angle3 = random.randint(1, 340 - (angle1 + angle2)) 318 319 sum_ = angle1 + angle2 + angle3 320 angle4 = 360 - sum_ 321 322 problem = f"Fourth angle of quadrilateral with angles ${angle1} , {angle2}, {angle3} =$" 323 solution = f'${angle4}$' 324 return problem, solution
Fourth Angle of Quadrilateral
| Ex. Problem | Ex. Solution |
|---|---|
| Fourth angle of quadrilateral with angles $162 , 43, 78 =$ | $77$ |
def
perimeter_of_polygons(max_sides=12, max_length=120):
327def perimeter_of_polygons(max_sides=12, max_length=120): 328 r"""Perimeter of Polygons 329 330 | Ex. Problem | Ex. Solution | 331 | --- | --- | 332 | The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is: | $319$ | 333 """ 334 size_of_sides = random.randint(3, max_sides) 335 sides = [random.randint(1, max_length) for _ in range(size_of_sides)] 336 337 problem = f"The perimeter of a ${size_of_sides}$ sided polygon with lengths of ${', '.join(map(str, sides))}$cm is: " 338 solution = sum(sides) 339 340 return problem, f'${solution}$'
Perimeter of Polygons
| Ex. Problem | Ex. Solution |
|---|---|
| The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is: | $319$ |
def
pythagorean_theorem(max_length=20):
343def pythagorean_theorem(max_length=20): 344 """Pythagorean Theorem 345 346 | Ex. Problem | Ex. Solution | 347 | --- | --- | 348 | What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$? | $13.45$ | 349 """ 350 a = random.randint(1, max_length) 351 b = random.randint(1, max_length) 352 c = round((a**2 + b**2)**0.5, 2) 353 354 problem = f"What is the hypotenuse of a right triangle given the other two sides have lengths ${a}$ and ${b}$?" 355 solution = f"${c}$" 356 return problem, solution
Pythagorean Theorem
| Ex. Problem | Ex. Solution |
|---|---|
| What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$? | $13.45$ |
def
radian_to_deg(max_rad=6.28):
359def radian_to_deg(max_rad=6.28): 360 """Radians to Degrees""" 361 a = random.randint(0, int(max_rad * 100)) / 100 362 b = round((180 * a) / math.pi, 2) 363 364 problem = f"Angle ${a}$ radians in degrees is: " 365 solution = f'${b}$' 366 return problem, solution
Radians to Degrees
def
sector_area(max_radius=49, max_angle=359):
369def sector_area(max_radius=49, max_angle=359): 370 """Area of a Sector 371 372 | Ex. Problem | Ex. Solution | 373 | --- | --- | 374 | What is the area of a sector with radius $42$ and angle $83$ degrees? | $1277.69$ | 375 """ 376 r = random.randint(1, max_radius) 377 a = random.randint(1, max_angle) 378 secArea = float((a / 360) * math.pi * r * r) 379 formatted_float = round(secArea, 2) 380 381 problem = f"What is the area of a sector with radius ${r}$ and angle ${a}$ degrees?" 382 solution = f"${formatted_float}$" 383 return problem, solution
Area of a Sector
| Ex. Problem | Ex. Solution |
|---|---|
| What is the area of a sector with radius $42$ and angle $83$ degrees? | $1277.69$ |
def
sum_of_polygon_angles(max_sides=12):
386def sum_of_polygon_angles(max_sides=12): 387 """Sum of Angles of Polygon 388 389 | Ex. Problem | Ex. Solution | 390 | --- | --- | 391 | What is the sum of interior angles of a polygon with $8$ sides? | $1080$ | 392 """ 393 side_count = random.randint(3, max_sides) 394 sum = (side_count - 2) * 180 395 396 problem = f"What is the sum of interior angles of a polygon with ${side_count}$ sides?" 397 return problem, f'${sum}$'
Sum of Angles of Polygon
| Ex. Problem | Ex. Solution |
|---|---|
| What is the sum of interior angles of a polygon with $8$ sides? | $1080$ |
def
surface_area_cone(max_radius=20, max_height=50, unit='m'):
400def surface_area_cone(max_radius=20, max_height=50, unit='m'): 401 """Surface area of a cone 402 403 | Ex. Problem | Ex. Solution | 404 | --- | --- | 405 | Surface area of cone with height $= 26m$ and radius $= 6m$ is | $616 m^2$ | 406 """ 407 a = random.randint(1, max_height) 408 b = random.randint(1, max_radius) 409 410 slopingHeight = math.sqrt(a**2 + b**2) 411 ans = int(math.pi * b * slopingHeight + math.pi * b * b) 412 413 problem = f"Surface area of cone with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 414 solution = f"${ans} {unit}^2$" 415 return problem, solution
Surface area of a cone
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of cone with height $= 26m$ and radius $= 6m$ is | $616 m^2$ |
def
surface_area_cube(max_side=20, unit='m'):
418def surface_area_cube(max_side=20, unit='m'): 419 """Surface area of a cube 420 421 | Ex. Problem | Ex. Solution | 422 | --- | --- | 423 | Surface area of cube with side $= 6m$ is | $216 m^2$ | 424 """ 425 a = random.randint(1, max_side) 426 ans = 6 * (a**2) 427 428 problem = f"Surface area of cube with side $= {a}{unit}$ is" 429 solution = f"${ans} {unit}^2$" 430 return problem, solution
Surface area of a cube
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of cube with side $= 6m$ is | $216 m^2$ |
def
surface_area_cuboid(max_side=20, unit='m'):
433def surface_area_cuboid(max_side=20, unit='m'): 434 """Surface area of a cuboid 435 436 | Ex. Problem | Ex. Solution | 437 | --- | --- | 438 | Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is | $936 m^2$ | 439 """ 440 a = random.randint(1, max_side) 441 b = random.randint(1, max_side) 442 c = random.randint(1, max_side) 443 ans = 2 * (a * b + b * c + c * a) 444 445 problem = f"Surface area of cuboid with sides of lengths: ${a}{unit}, {b}{unit}, {c}{unit}$ is" 446 solution = f"${ans} {unit}^2$" 447 return problem, solution
Surface area of a cuboid
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is | $936 m^2$ |
def
surface_area_cylinder(max_radius=20, max_height=50, unit='m'):
450def surface_area_cylinder(max_radius=20, max_height=50, unit='m'): 451 """Surface area of a cylinder 452 453 | Ex. Problem | Ex. Solution | 454 | --- | --- | 455 | Surface area of cylinder with height $= 26m$ and radius $= 15m$ is | $3864 m^2$ | 456 """ 457 a = random.randint(1, max_height) 458 b = random.randint(1, max_radius) 459 ans = int(2 * math.pi * a * b + 2 * math.pi * b * b) 460 461 problem = f"Surface area of cylinder with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 462 solution = f"${ans} {unit}^2$" 463 return problem, solution
Surface area of a cylinder
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of cylinder with height $= 26m$ and radius $= 15m$ is | $3864 m^2$ |
def
surface_area_pyramid(unit='m'):
466def surface_area_pyramid(unit='m'): 467 """Surface area of a pyramid 468 469 | Ex. Problem | Ex. Solution | 470 | --- | --- | 471 | Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is | $2400 m^2$ | 472 """ 473 # List of Pythagorean triplets 474 _PYTHAGOREAN = [(3, 4, 5), (6, 8, 10), (9, 12, 15), (12, 16, 20), 475 (15, 20, 25), (5, 12, 13), (10, 24, 26), (7, 24, 25)] 476 477 # Generate first triplet 478 height, half_width, _ = random.sample( 479 random.choice(_PYTHAGOREAN), 3) 480 481 # Calculate the first triangle height 482 triangle_height_1 = math.sqrt((half_width)**2 + height**2) 483 484 # Generate second triplet 485 second_triplet = random.choice([i for i in _PYTHAGOREAN if height in i]) 486 half_length, _ = random.sample( 487 tuple(i for i in second_triplet if i != height), 2) 488 489 # Calculate the second triangle height 490 triangle_height_2 = math.sqrt((half_length)**2 + height**2) 491 492 # Calculate triangles area 493 triangle_1 = half_length * triangle_height_1 494 triangle_2 = half_width * triangle_height_2 495 496 # Calculate base area 497 base = 4 * half_width * half_length 498 ans = base + 2 * triangle_1 + 2 * triangle_2 499 500 problem = f"Surface area of pyramid with base length $= {2*half_length}{unit}$, base width $= {2*half_width}{unit}$, and height $= {height}{unit}$ is" 501 solution = f"${ans} {unit}^2$" 502 return problem, solution
Surface area of a pyramid
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is | $2400 m^2$ |
def
surface_area_sphere(max_side=20, unit='m'):
505def surface_area_sphere(max_side=20, unit='m'): 506 """Surface area of a sphere 507 508 | Ex. Problem | Ex. Solution | 509 | --- | --- | 510 | Surface area of a sphere with radius $= 8m$ is | $804.25 m^2$ | 511 """ 512 r = random.randint(1, max_side) 513 ans = round(4 * math.pi * r * r, 2) 514 515 problem = f"Surface area of a sphere with radius $= {r}{unit}$ is" 516 solution = f"${ans} {unit}^2$" 517 return problem, solution
Surface area of a sphere
| Ex. Problem | Ex. Solution |
|---|---|
| Surface area of a sphere with radius $= 8m$ is | $804.25 m^2$ |
def
third_angle_of_triangle(max_angle=89):
520def third_angle_of_triangle(max_angle=89): 521 """Third Angle of Triangle 522 523 | Ex. Problem | Ex. Solution | 524 | --- | --- | 525 | Third angle of triangle with angles $10$ and $22 =$ | $148$ | 526 """ 527 angle1 = random.randint(1, max_angle) 528 angle2 = random.randint(1, max_angle) 529 angle3 = 180 - (angle1 + angle2) 530 531 problem = f"Third angle of triangle with angles ${angle1}$ and ${angle2} = $" 532 return problem, f'${angle3}$'
Third Angle of Triangle
| Ex. Problem | Ex. Solution |
|---|---|
| Third angle of triangle with angles $10$ and $22 =$ | $148$ |
def
valid_triangle(max_side_length=50):
535def valid_triangle(max_side_length=50): 536 """Valid Triangle 537 538 | Ex. Problem | Ex. Solution | 539 | --- | --- | 540 | Does triangel with sides $10, 31$ and $14$ exist? | No | 541 """ 542 sideA = random.randint(1, max_side_length) 543 sideB = random.randint(1, max_side_length) 544 sideC = random.randint(1, max_side_length) 545 546 sideSums = [sideA + sideB, sideB + sideC, sideC + sideA] 547 sides = [sideC, sideA, sideB] 548 549 exists = True & (sides[0] < sideSums[0]) & (sides[1] < sideSums[1]) & ( 550 sides[2] < sideSums[2]) 551 552 problem = f"Does triangle with sides ${sideA}, {sideB}$ and ${sideC}$ exist?" 553 solution = "Yes" if exists else "No" 554 return problem, f'${solution}$'
Valid Triangle
| Ex. Problem | Ex. Solution |
|---|---|
| Does triangel with sides $10, 31$ and $14$ exist? | No |
def
volume_cone(max_radius=20, max_height=50, unit='m'):
557def volume_cone(max_radius=20, max_height=50, unit='m'): 558 """Volume of a cone 559 560 | Ex. Problem | Ex. Solution | 561 | --- | --- | 562 | Volume of cone with height $= 44m$ and radius $= 11m$ is | $5575 m^3$ | 563 """ 564 a = random.randint(1, max_height) 565 b = random.randint(1, max_radius) 566 ans = int(math.pi * b * b * a * (1 / 3)) 567 568 problem = f"Volume of cone with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 569 solution = f"${ans} {unit}^3$" 570 return problem, solution
Volume of a cone
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of cone with height $= 44m$ and radius $= 11m$ is | $5575 m^3$ |
def
volume_cube(max_side=20, unit='m'):
573def volume_cube(max_side=20, unit='m'): 574 """Volume of a cube 575 576 | Ex. Problem | Ex. Solution | 577 | --- | --- | 578 | Volume of a cube with a side length of $19m$ is | $6859 m^3$ | 579 """ 580 a = random.randint(1, max_side) 581 ans = a**3 582 583 problem = f"Volume of cube with a side length of ${a}{unit}$ is" 584 solution = f"${ans} {unit}^3$" 585 return problem, solution
Volume of a cube
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of a cube with a side length of $19m$ is | $6859 m^3$ |
def
volume_cuboid(max_side=20, unit='m'):
588def volume_cuboid(max_side=20, unit='m'): 589 """Volume of a cuboid 590 591 | Ex. Problem | Ex. Solution | 592 | --- | --- | 593 | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ | 594 """ 595 a = random.randint(1, max_side) 596 b = random.randint(1, max_side) 597 c = random.randint(1, max_side) 598 ans = a * b * c 599 600 problem = f"Volume of cuboid with sides = ${a}{unit}, {b}{unit}, {c}{unit}$ is" 601 solution = f"${ans} {unit}^3$" 602 return problem, solution
Volume of a cuboid
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ |
def
volume_cylinder(max_radius=20, max_height=50, unit='m'):
605def volume_cylinder(max_radius=20, max_height=50, unit='m'): 606 """Volume of a cylinder 607 608 | Ex. Problem | Ex. Solution | 609 | --- | --- | 610 | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ | 611 """ 612 a = random.randint(1, max_height) 613 b = random.randint(1, max_radius) 614 ans = int(math.pi * b * b * a) 615 616 problem = f"Volume of cylinder with height $= {a}{unit}$ and radius $= {b}{unit}$ is" 617 solution = f"${ans} {unit}^3$" 618 return problem, solution
Volume of a cylinder
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ |
def
volume_cone_frustum(max_r1=20, max_r2=20, max_height=50, unit='m'):
621def volume_cone_frustum(max_r1=20, max_r2=20, max_height=50, unit='m'): 622 """Volume of the frustum of a cone 623 624 | Ex. Problem | Ex. Solution | 625 | --- | --- | 626 | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ | 627 """ 628 h = random.randint(1, max_height) 629 r1 = random.randint(1, max_r1) 630 r2 = random.randint(1, max_r2) 631 ans = round(((math.pi * h) * (r1**2 + r2**2 + r1 * r2)) / 3, 2) 632 633 problem = f"Volume of frustum with height $= {h}{unit}$ and $r1 = {r1}{unit}$ is and $r2 = {r2}{unit}$ is " 634 solution = f"${ans} {unit}^3$" 635 return problem, solution
Volume of the frustum of a cone
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ |
def
volume_hemisphere(max_radius=100):
638def volume_hemisphere(max_radius=100): 639 """Volume of a hemisphere 640 641 | Ex. Problem | Ex. Solution | 642 | --- | --- | 643 | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ | 644 """ 645 r = random.randint(1, max_radius) 646 ans = round((2 * math.pi / 3) * r**3, 2) 647 648 problem = f"Volume of hemisphere with radius ${r} m =$ " 649 solution = f"${ans} m^3$" 650 return problem, solution
Volume of a hemisphere
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ |
def
volume_pyramid(max_length=20, max_width=20, max_height=50, unit='m'):
653def volume_pyramid(max_length=20, max_width=20, max_height=50, unit='m'): 654 """Volume of a pyramid 655 656 | Ex. Problem | Ex. Solution | 657 | --- | --- | 658 | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ | 659 """ 660 length = random.randint(1, max_length) 661 width = random.randint(1, max_width) 662 height = random.randint(1, max_height) 663 664 ans = round((length * width * height) / 3, 2) 665 666 problem = f"Volume of pyramid with base length $= {length} {unit}$, base width $= {width} {unit}$ and height $= {height} {unit}$ is" 667 solution = f"${ans} {unit}^3$" 668 return problem, solution
Volume of a pyramid
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ |
def
volume_sphere(max_radius=100):
671def volume_sphere(max_radius=100): 672 """Volume of a sphere 673 674 | Ex. Problem | Ex. Solution | 675 | --- | --- | 676 | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ | 677 """ 678 r = random.randint(1, max_radius) 679 ans = round((4 * math.pi / 3) * r**3, 2) 680 681 problem = f"Volume of sphere with radius ${r} m = $" 682 solution = f"${ans} m^3$" 683 return problem, solution
Volume of a sphere
| Ex. Problem | Ex. Solution |
|---|---|
| Volume of sphere with radius $30 m = $ | $113097.36 m^3$ |