category stringclasses 3
values | subcategory stringclasses 18
values | question stringlengths 4 629 | answer float64 -273,260,096,089 713,712,038B | reasoning stringlengths 9 516 ⌀ | source stringclasses 6
values |
|---|---|---|---|---|---|
Geometry | geometry | the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ? | 13 | n0 = 23.0
n1 = 10.0
answer = n0 - n1
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of square field whose side of length 8 m ? | 64 | n0 = 8.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ? | 1,392 | import math
n0 = 36.0
n1 = 58.0
t0 = math.sqrt(max(0, n0))
t1 = 4 * t0
answer = n1 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is 5 more than the width . what are the dimensions of the rectangle if the perimeter is 34 ? | 11 | n0 = 5.0
n1 = 34.0
t0 = n1 / 2.0
t1 = n0 + t0
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a crate measures 3 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still... | 3 | n0 = 3.0
n1 = 8.0
n2 = 12.0
t0 = n1 * n2
t1 = n0 * t0
t2 = t1 / n2
answer = t2 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | a box is in the shape of a semicircle with a radius of 12 . what is the approximate perimeter of the semicircle ? | 61.699112 | n0 = 12.0
t0 = n0 * 3.141592653589793
t1 = n0 * 2.0
answer = t0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ? | 8 | n0 = 64.0
t0 = n0 / 4.0
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a heig... | 0.025 | import math
n0 = 100.0
n1 = 25.0
n2 = 5.0
n3 = 10.0
t0 = math.pi * n0**2
t1 = math.pi * n2**2 * n3
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number . | 4 | import math
n0 = 6.5
t0 = 6 * n0**2 # surface of a cube
t1 = t0 / 4.0
t2 = t1 / 3.141592653589793
t3 = math.sqrt(max(0, t2))
answer = math.floor(t3)
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 588 sq m , then what is the breadth of the rectangular plot ? | 14 | import math
n0 = 588.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour . if the empty rectangular box is 5 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the box ? | 20 | n0 = 3.0
n1 = 5.0
n2 = 4.0
n3 = 3.0
t0 = n1 * n2
t1 = n3 * t0
answer = t1 / n0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the sum of divisors of 544 which are perfect squares | 21 | import math
n0 = 544.0
t0 = n0 / 2.0
t1 = t0 / 2.0
t2 = t1 / 2.0
t3 = t2 / 2.0
t4 = t3 / 2.0
t5 = n0 / t4
t6 = t5 / 2.0
t7 = math.sqrt(max(0, t6))
t8 = t7 + 1.0
answer = t8 + t6
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area q of that hemisphere ? | 9 | n0 = 4.0
n1 = 2.0
n2 = 3.0
t0 = n2 / 3.141592653589793
t1 = n0 * 3.141592653589793
t2 = t0 * t1
t3 = t0 * 3.141592653589793
t4 = t2 / n1
answer = t4 + t3
print(answer) | MathQA_Geometry |
Geometry | geometry | frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ? | 64 | n0 = 40.0
n1 = 480.0
t0 = n1 / n0
t1 = t0 + t0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ? | 675 | n0 = 120.0
t0 = 2.0 * 3.0
t1 = 1.0 * 2.0
t2 = t0 + t1
t3 = n0 / t2
t4 = t3 * 3.0
answer = t3 * t4
print(answer) | MathQA_Geometry |
Geometry | geometry | you buy a piece of land with an area of â ˆ š 1024 , how long is one side of the land plot ? | 32 | import math
n0 = 1024.0
answer = math.sqrt(max(0, n0))
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 528 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ? | 17,254.94231 | import math
n0 = 528.0
n1 = 704.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is : | 9 | import math
n0 = 12.0
n1 = 20.0
n2 = 6.75
t0 = 1.0 / 3.0
t1 = 4.0 * 3.141592653589793
t2 = math.pi * n0**2 * n2
t3 = t2 * 3.0
t4 = t3 / t1
answer = t4**min(t0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters , what is the length of the rectangle , in centimeters ? | 2 | n0 = 4.0
n1 = 8.0
t0 = n0**min(2.0, 5)
answer = t0 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of a square field whose diagonal of length 30 m ? | 450 | n0 = 30.0
t0 = n0**2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in an electric circuit , two resistors with resistances 8 ohms and 9 ohms are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is r value ? | 4.235294 | n0 = 8.0
n1 = 9.0
t0 = n0 + n1
t1 = n0 * n1
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately | 2,970.962591 | import math
n0 = 17.56
n1 = 2.0
t0 = n0 / 3.141592653589793
t1 = math.sqrt(max(0, t0))
t2 = t1 * 100.0
t3 = 2 * math.pi * t2
answer = t3 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field . | 120 | import math
n0 = 15.0
n1 = 17.0
t0 = n1**min(2.0, 5)
t1 = n0**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
answer = n0 * t3 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles . | 4,313.735578 | import math
n0 = 264.0
n1 = 352.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | three runners running around a circular track can complete one revolution in 2 , 4 and 5.5 respectively . when will they meet at starting point ? | 44 | n0 = 2.0
n1 = 4.0
n2 = 5.5
t0 = n0 * n1
answer = n2 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sum of a number and its square is 272 , what is the number ? | 16 | import math
n0 = 272.0
t0 = math.sqrt(max(0, n0))
answer = math.floor(t0)
print(answer) | MathQA_Geometry |
Geometry | geometry | a certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water . if between 6 and 13 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately | 4.020726 | n0 = 80.0
n1 = 90.0
n2 = 6.0
n3 = 13.0
t0 = n3 * 100.0
t1 = 100.0 - n0
t2 = t0 / t1
answer = t2**(1 / 3)
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ? | 340 | n0 = 36.0
n1 = 34.0
n2 = 20.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | 14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? | 189 | n0 = 14.0
n1 = 7.0
t0 = n0 * n1
t1 = n0 - 1.0
t2 = n0 * t1
t3 = t2 / 2.0
answer = t3 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet . what is its area , in square feet ? | 4,800 | n0 = 560.0
n1 = 100.0
t0 = 2.0 + 3.0
t1 = n1 / t0
t2 = t1 * 3.0
t3 = t1 * 4.0
answer = t2 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of a triangle is 32 cm and the inradius of the triangle is 3.5 cm . what is the area of the triangle ? | 56 | n0 = 32.0
n1 = 3.5
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and de = 13 cm , then find the length of bc . | 5 | import math
n0 = 144.0
n1 = 25.0
n2 = 13.0
t0 = n0 + n1
t1 = n1 / t0
t2 = math.sqrt(max(0, t1))
answer = n2 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the cost of painting the whole surface area of a cube at the rate of 13 paise per sq . cm is rs . 343.98 . then the volume of the cube is | 9,261 | import math
n0 = 13.0
n1 = 343.98
t0 = n0 / 100.0
t1 = 2.0 * 3.0
t2 = n1 / t0
t3 = t2 / t1
t4 = math.sqrt(max(0, t3))
answer = t4**3
print(answer) | MathQA_Geometry |
Geometry | geometry | if the diameter of circle r is 60 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ? | 36 | import math
n0 = 60.0
t0 = math.pi * n0**2
t1 = math.pi * 100.0**2
t2 = t0 * 100.0
answer = t2 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a rhombus is 28 m and length of one of its diagonals is 12 m . the area of the rhombus is ? | 328.195064 | import math
n0 = 28.0
n1 = 12.0
t0 = n0 * 2.0
t1 = n1**min(2.0, 5)
t2 = t0**min(2.0, 5)
t3 = t2 - t1
t4 = math.sqrt(max(0, t3))
t5 = n1 * t4
answer = t5 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years... | 12,544 | n0 = 1.0
n1 = 223.0
t0 = n1 - n0
t1 = t0 / 2.0
t2 = t1**min(2.0, 5)
answer = n1 + t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % | 44 | n0 = 20.0
t0 = n0 + 100.0
t1 = t0 / 100.0
t2 = t1 * t1
t3 = t2 - 1.0
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumference of a circle is equal to 72 pi . find the radius of this circle . | 36 | n0 = 72.0
answer = n0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a triangle is with base 2 m and height 3 m ? | 3 | n0 = 2.0
n1 = 3.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the height of a cone is increased by 130 % then its volume is increased by ? | 130 | n0 = 130.0
answer = n0 * 1.0 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of the largest circle that can be drawn inside a square of side 70 cm in length is : | 3,848.451001 | import math
n0 = 70.0
t0 = n0 / 2.0
answer = math.pi * t0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ? | 113.097336 | n0 = 36.0
n1 = 20.0
n2 = 12.0
t0 = n2**min(2.0, 5)
t1 = t0 * 3.141592653589793
answer = t1 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the smallest number that should be multiplied with 54000 to make it a perfect cube . | 4 | n0 = 54000.0
t0 = n0 / 1000.0
t1 = t0 / 3.0
t2 = t1 / 3.0
t3 = t2 / 3.0
answer = t3 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | the edge of three cubes of metal is 3 dm , 4 dm and 5 dm . they are melted and formed into a single cube . find the edge of the new cube ? | 6 | n0 = 3.0
n1 = 4.0
n2 = 5.0
answer = 2.0 * 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a parallelogram is 450 sq m and its altitude is twice the corresponding base . then the length of the base is ? | 15 | import math
n0 = 450.0
t0 = n0 / 2.0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of a square field whose diagonal of length 40 m ? | 800 | n0 = 40.0
t0 = n0**2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ? | 0.111111 | n0 = 2.0
n1 = 0.0
n2 = 8.0
n3 = 12.0
n4 = 14.0
n5 = 0.0
n6 = 6.0
n7 = 0.0
n8 = 8.0
n9 = 4.0
n10 = 10.0
n11 = 0.0
t0 = 10.0 + 2.0
t1 = 4.0**min(2.0, 5)
t2 = t1 / 2.0
t3 = t0**min(2.0, 5)
t4 = t3 / 2.0
answer = t2 / t4
print(answer) | MathQA_Geometry |
Geometry | geometry | two equal triangles constitute rhombus a . if the diagonals of rhombus are 15 cm and 20 cm long . what is the area of each triangle ? | 75 | n0 = 15.0
n1 = 20.0
t0 = n0 * n1
answer = t0 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 432 sq meters , then what is the width ( in meters ) of the rectangular plot ? | 12 | n0 = 432.0
t0 = n0 / 3.0
t1 = t0 / 3.0
answer = t1 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | susan made a block with small cubes of 8 cubic cm volume to make a block , 3 small cubes long , 9 small cubes wide and 5 small cubes deep . she realizes that she has used more small cubes than she really needed . she realized that she could have glued a fewer number of cubes together to lock like a block with same dime... | 114 | n0 = 8.0
n1 = 3.0
n2 = 9.0
n3 = 5.0
t0 = 3.0 + 4.0
t1 = n2 * 1.0
t2 = n3 * t1
t3 = t0 * 3.0
t4 = t2 - t3
t5 = t2 + t4
answer = t5 + t2
print(answer) | MathQA_Geometry |
Geometry | geometry | in a certain parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle ? | 65 | n0 = 50.0
t0 = 3600.0 / 10.0
t1 = n0 * 2.0
t2 = t0 - t1
answer = t2 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | 6,342 | n0 = 25.0
n1 = 15.0
n2 = 12.0
n3 = 7.0
n4 = 6.0
n5 = 3.0
n6 = 4.0
n7 = 3.0
t0 = n0 + n1
t1 = n2 * 2.0
t2 = n4 * n5
t3 = n5 * n6
t4 = t0 * t1
t5 = n5 * t3
t6 = t4 - t2
t7 = t6 - t5
answer = n3 * t7
print(answer) | MathQA_Geometry |
Geometry | geometry | if a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet , what is the length of each of the shorter sides ? | 7 | import math
n0 = 91.0
n1 = 40.0
t0 = n1 / 2.0
t1 = n0 * 4.0
t2 = t0**min(2.0, 5)
t3 = t2 - t1
t4 = math.sqrt(max(0, t3))
t5 = t0 - t4
answer = t5 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cubic object 3 ' ' x 3 ' ' x 3 ' ' is painted blue on all the outside surfaces , including the top and bottom . if the cube is cut into 27 cubes of 1 ' ' x 1 ' ' x 1 ' ' , how many 1 ' ' cubes do have any painted surfaces ? | 26 | n0 = 3.0
n1 = 3.0
n2 = 3.0
n3 = 27.0
n4 = 1.0
n5 = 1.0
n6 = 1.0
n7 = 1.0
answer = n3 - 1.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 9 , 0 ) , ( 0 , - 3.5 ) , ( - 9 , 0 ) ? | 63 | n0 = 0.0
n1 = 3.5
n2 = 9.0
n3 = 0.0
n4 = 0.0
n5 = 3.5
n6 = 9.0
n7 = 0.0
t0 = n2 * 2.0
t1 = n1 * 2.0
answer = t0 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | 12 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? | 150 | n0 = 12.0
n1 = 7.0
t0 = n0 * n1
t1 = n0 - 1.0
t2 = n0 * t1
t3 = t2 / 2.0
answer = t3 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the measure of the angle e made by the diagonals of the any adjacent sides of a cube . | 60 |
answer = 180.0 / 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x and y coordinates of p , q and r are to be integers that satisfy the inequalitites - 4 ≤ x ≤ 5 and 6 ≤ y ≤ 16 . how many different triangles with these properties could be constructed ? | 9,900 | n0 = 4.0
n1 = 5.0
n2 = 6.0
n3 = 16.0
t0 = n0 + n2
t1 = n3 - n1
t2 = 10.0 - 1.0
t3 = t0 * t1
t4 = t3 * t2
answer = t4 * 10.0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the ratio between perimeters of two squares one having 11 times the diagonal then the other ? | 11 | n0 = 11.0
t0 = n0 / n0
answer = n0 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the points a ( 0 , 0 ) , b ( 0 , 4 a - 2 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ? | 63 | n0 = 0.0
n1 = 0.0
n2 = 0.0
n3 = 4.0
n4 = 2.0
n5 = 2.0
n6 = 1.0
n7 = 2.0
n8 = 6.0
n9 = 90.0
t0 = n4 + n8
t1 = n3 - n4
t2 = t0 / n4
t3 = t2 * t1
t4 = n3 * t2
t5 = t3 + 1.0
t6 = t4 - n4
t7 = t5 * t6
answer = t7 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a clockwise rotation around point z ( that is , a rotation in the direction of the arrow ) transforms the shaded quadrilateral to the unshaded quadrilateral . the angle of rotation is approximately | 270 | t0 = 3600.0 / 10.0
t1 = t0 / 4.0
answer = t0 - t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before ... | 9 | import math
n0 = 126.0
n1 = 2.0
n2 = 4.0
n3 = 126.0
t0 = n0 * n1
t1 = -n2
t2 = n2**min(2.0, 5)
t3 = n2 * t0
t4 = t3 + t2
t5 = math.sqrt(max(0, t4))
t6 = t1 + t5
t7 = t6 / 2.0
answer = n0 / t7
print(answer) | MathQA_Geometry |
Geometry | geometry | a box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ? | 40 | n0 = 36.0
n1 = 45.0
n2 = 18.0
t0 = n2 / 2.0
t1 = n0 * n1
t2 = n2 * t1
t3 = t0**3
answer = t2 / t3
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is : | 6 | import math
n0 = 12.0
t0 = n0 / 2.0
t1 = 4.0 * 3.141592653589793
t2 = n0 * t0
t3 = t2 * 3.141592653589793
t4 = t3 * 2.0
t5 = t4 / t1
answer = math.sqrt(max(0, t5))
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonals of a rhombus are 25 cm and 30 cm . find its area ? | 375 | n0 = 25.0
n1 = 30.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of one face of a cube is 24 cm . its volume will be : | 216 | n0 = 24.0
t0 = n0 / 4. # square edge given perimeter
answer = t0**3
print(answer) | MathQA_Geometry |
Geometry | geometry | rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 3 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ? | 0.444444 | n0 = 2.0
n1 = 3.0
t0 = n0**min(2.0, 5)
t1 = n1**min(2.0, 5)
answer = t0 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | one side of a rectangular field is 14 m and one of its diagonal is 17 m . find the area of the field . | 135.011111 | import math
n0 = 14.0
n1 = 17.0
t0 = n1**min(2.0, 5)
t1 = n0**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
answer = n0 * t3 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | if the side length of square b is four times that of square a , the area of square b is how many times the area of square a ? | 16 |
answer = 4.0 * 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | 8,154 | n0 = 25.0
n1 = 15.0
n2 = 12.0
n3 = 9.0
n4 = 6.0
n5 = 3.0
n6 = 4.0
n7 = 3.0
t0 = n0 + n1
t1 = n2 * 2.0
t2 = n4 * n5
t3 = n5 * n6
t4 = t0 * t1
t5 = n5 * t3
t6 = t4 - t2
t7 = t6 - t5
answer = n3 * t7
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 132 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ? | 8,473.40917 | import math
n0 = 132.0
n1 = 352.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ? | 130 | n0 = 10.0
n1 = 600.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 60 cm , find the sum of the perimeters of all the triangles... | 360 | n0 = 2.0
n1 = 1.0
n2 = 3.0
n3 = 2.0
n4 = 1.0
n5 = 60.0
t0 = n5 + n5 + n5 # perimeter of a triangle
answer = t0 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a square is increased by 5 % then how much % does its area increases ? | 10.25 | n0 = 5.0
t0 = n0 + 100.0
t1 = 100.0**2
t2 = t0**2
t3 = t2 - t1
t4 = t3 * 100.0
answer = t4 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 660 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ? | 4,775.921532 | import math
n0 = 660.0
n1 = 704.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | which is the smallest number divides 2800 and gives a perfect square . | 7 | n0 = 2800.0
t0 = 2.0 + 3.0
t1 = n0 / 2.0
t2 = t1 / 2.0
t3 = t2 / 2.0
t4 = t3 / 2.0
t5 = t4 / t0
answer = t5 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is : | 2 | n0 = 8.0
n1 = 1.0
answer = n0**(1 / 3)
print(answer) | MathQA_Geometry |
Geometry | geometry | in a parallelogram , the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively . find its area | 600 | n0 = 30.0
n1 = 20.0
answer = n0 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | an error 2 % in excess ismade while measuring the side ofa square . the % of error in the calculated area of the square is ? | 4.04 | n0 = 2.0
t0 = n0 + 100.0
t1 = 100.0 * 100.0
t2 = t0 * t0
t3 = t2 - t1
answer = t3 / 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side | 876 | n0 = 36.5
n1 = 1.0
n2 = 16.0
n3 = 8.0
t0 = 6 * n3**2 # surface of a cube
t1 = t0 / n2
answer = n0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ? | 5,100 | n0 = 120.0
n1 = 60.0
n2 = 10.0
n3 = 3.0
t0 = n0 + n1
t1 = t0 - n2
t2 = n2 * t1
answer = n3 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of a parallelogram with base 26 cm and height 12 cm ? | 312 | n0 = 26.0
n1 = 12.0
answer = n0 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is | 1,200 | n0 = 15.0
n1 = 12.0
t0 = n1 * 2.0
t1 = n0 * 2.0
t2 = n0 * n1 # area of rectangle
t3 = t0 + t1
t4 = t2 * 2.0
t5 = t4 / t3
answer = n0 * n1 * t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a square is increased by 10 % then how much % does its area increases ? | 21 | n0 = 10.0
t0 = n0 + 100.0
t1 = 100.0**2
t2 = t0**2
t3 = t2 - t1
t4 = t3 * 100.0
answer = t4 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | if circles x and y have the same area and circle x has a circumference of 14 π , half of the radius of circle y is : | 3.5 | n0 = 14.0
t0 = n0 / 2.0
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the curved surface area , if the radius of a cone is 35 m and slant height is 30 m ? | 3,298.672286 | n0 = 35.0
n1 = 30.0
t0 = n0 * n1
answer = t0 * 3.141592653589793
print(answer) | MathQA_Geometry |
Geometry | geometry | if the area of a square with sides of length 12 centimeters is equal to the area of a rectangle with a width of 6 centimeters , what is the length of the rectangle , in centimeters ? | 24 | n0 = 12.0
n1 = 6.0
t0 = n0**min(2.0, 5)
answer = t0 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | in an electric circuit , three resistors with resistances 2 ohms , 5 ohms and 6 ohms are connected in parallel . in this case , if r is the combined resistance of these three resistors , then the reciprocal of r is equal to the sum of the reciprocals resistors . what is r value ? | 0.866667 | n0 = 2.0
n1 = 5.0
n2 = 6.0
t0 = 1.0 / n0
t1 = 1.0 / n1
t2 = 1.0 / n2
t3 = t0 + t1
answer = t3 + t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ? | 25 | n0 = 20.0
n1 = 2.5
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | in front of you lies a figure made up with 20 x 10 square blocks . will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares ? | 11,550 | n0 = 20.0
n1 = 10.0
t0 = n0 + 1.0
t1 = n1 + 1.0
t2 = n0 * t0
t3 = n1 * t1
t4 = t2 / 2.0
t5 = t3 / 2.0
answer = t4 * t5
print(answer) | MathQA_Geometry |
Geometry | geometry | a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many j cubes are painted on only 2 faces ? | 12 | n0 = 27.0
n1 = 2.0
t0 = 1.0 / 3.0
t1 = n0**min(t0, 5)
answer = t1 * 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | one side of a rectangular field is 16 m and one of its diagonal is 17 m . find the area of the field . | 91.913002 | import math
n0 = 16.0
n1 = 17.0
t0 = n1**min(2.0, 5)
t1 = n0**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
answer = n0 * t3 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | an entry in an unshaded square is obtained by adding the entries connected to it from the row above ( 11 is one such number ) . write the value of n ? | 10 | n0 = 11.0
t0 = n0 * 3.0
t1 = t0 - 3.0
answer = t1 / 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ? | 7,737.76985 | import math
n0 = 56.0
t0 = 2 * math.pi * n0
t1 = t0 / 4.0
answer = t1**min(2.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ? | 27 | import math
n0 = 7.0
n1 = 4.0
t0 = 2.0 * 4.0
t1 = n0 * 2.0
t2 = t0 + 1.0
t3 = t1 + 1.0
t4 = t2 / 2.0
t5 = t3 / 2.0
t6 = t5**min(2.0, 5)
t7 = t4**min(2.0, 5)
t8 = t6 - t7
t9 = math.sqrt(max(0, t8))
answer = t4 * t9 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ? | 28 | n0 = 21.0
t0 = 4.0 - 1.0
t1 = n0 / t0
answer = t1 * 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of a square field whose diagonal of length 10 m ? | 50 | n0 = 10.0
t0 = n0**2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm . what is the area of the triangle ? | 30 | n0 = 20.0
n1 = 3.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle | 50 | n0 = 40.0
n1 = 2.5
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the radius of a circle that centers at the origin is 5 , how many points q on the circle have integer coordinates ? | 12 | n0 = 5.0
t0 = n0 + 4.0
t1 = n0 * n0
t2 = 2.0**min(2.0, 5)
t3 = t1 - t0
answer = t3 - t2
print(answer) | MathQA_Geometry |
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