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Geometry | geometry | a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 3 m , the volume of the box ( in m 3 ) is : | 3,780 | n0 = 48.0
n1 = 36.0
n2 = 3.0
n3 = 3.0
t0 = n2 * 2.0
t1 = n0 - t0
t2 = n1 - t0
answer = n2 * t1 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ? | 90 | n0 = 55.0
n1 = 9.0
n2 = 5.0
n3 = 4.0
n4 = 2.0
t0 = n0 + n1
t1 = n2 + t0
t2 = n3 + t1
t3 = n4 + t2
t4 = 100.0 - t3
t5 = t4 * 360.0
answer = t5 / 100.0
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 volume of 11248 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ? | 2,812 | n0 = 11248.0
n1 = 4.0
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 4 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 parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) | 26.703538 | import math
n0 = 20.0
n1 = 14.0
t0 = 2 * (n0 + n1) # perimetere of rectangle
t1 = t0 / 4. # square edge given perimeter
t2 = t1 / 2.0
t3 = 2 * math.pi * t2
answer = t3 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a lamp is put on one corner of a square plot of side 50 m . it ' s light reaches 21 m . find the area of that plot that is lit by that lamp ? | 346.36059 | import math
n0 = 50.0
n1 = 21.0
t0 = math.pi * n1**2
answer = t0 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a certain rectangular crate measures 12 feet by 16 feet by 18 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ? | 8 | import math
n0 = 12.0
n1 = 16.0
n2 = 18.0
t0 = n1 / 2.0
t1 = n0 * 3.141592653589793
t2 = math.pi * t0**2 * n0
t3 = t2 / t1
answer = math.sqrt(max(0, t3))
print(answer) | MathQA_Geometry |
Geometry | geometry | three table runners have a combined area of 224 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ? | 30 | n0 = 224.0
n1 = 80.0
n2 = 175.0
n3 = 24.0
t0 = n1 / 100.0
t1 = n0 - n3
t2 = n2 * t0
t3 = t1 - t2
answer = t3 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | 30 square stone slabs of equal size were needed to cover a floor area of 120 sq . m . find the length of each stone slab ? | 200 | import math
n0 = 30.0
n1 = 120.0
t0 = n1 / n0
t1 = math.sqrt(max(0, t0))
answer = t1 * 100.0
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 | the length of rectangle is thrice its breadth and its perimeter is 48 m , find the area of the rectangle ? | 108 | n0 = 48.0
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 | the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ? | 12.5 | n0 = 20.0
n1 = 10.0
n2 = 32.0
t0 = n0 * n1 # area of rectangle
t1 = t0 * 2.0
answer = t1 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | 2 corner most boxes of a chess board ( diagonally opposite ) haven been cut out there ' s a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ? ” | 30 | n0 = 2.0
n1 = 2.0
t0 = n0 * n0
t1 = t0 * t0
t2 = n0 * t1
answer = t2 - 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface of a cube is 150 sq cm . find its volume ? | 125 | import math
n0 = 150.0
t0 = 2.0 + 4.0
t1 = n0 / t0
t2 = math.sqrt(max(0, t1))
answer = t2**3
print(answer) | MathQA_Geometry |
Geometry | geometry | a steel vessel has a base of length 60 cm and breadth 30 cm . water is poured in the vessel . a cubical steel box having edge of 30 cm is immersed completely in the vessel . how much will the water rise ? | 15 | n0 = 60.0
n1 = 30.0
n2 = 30.0
t0 = n0 * n1
t1 = n1**min(3.0, 5)
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a square are multiplied by sqrt ( 5 ) , the area of the original square is how many times as large as the area of the resultant square ? | 20 | n0 = 5.0
answer = 4 * n0
print(answer) | MathQA_Geometry |
Geometry | geometry | if n is the smallest integer such that 432 times n is the square of an integer , what is the value of n ? | 3 | n0 = 432.0
t0 = n0 / 2.0
t1 = t0 / 2.0
t2 = t1 / 2.0
t3 = t2 / 2.0
t4 = t3 / 3.0
answer = t4 / 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is : | 140 | n0 = 19.0
n1 = 12.0
n2 = 2.0
t0 = n2 * n2
t1 = n0 * n1 # area of rectangle
t2 = n0 + t0
t3 = n1 + t0
t4 = t2 * t3 # area of rectangle
answer = t4 - t1
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 | find the perimeter and area of a square of side 13 cm . | 169 | n0 = 13.0
answer = n0**2
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 area of a parallelogram is 128 sq m . then the area of a triangle formed by its diagonal is - - - - - - - - - - ? | 64 | n0 = 128.0
answer = n0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ? | 12 | n0 = 8.0
n1 = 6.0
n2 = 48.0
n3 = 1.0
n4 = 1.0
t0 = n0 + n1
answer = t0 - 2.0
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 area of a rectangular plot is 360 square metres . if the length is 25 % less than the breadth , what is the breadth of the plot ? | 21.908902 | import math
n0 = 360.0
n1 = 25.0
t0 = n1 / 100.0
t1 = 1.0 - t0
t2 = n0 / t1
answer = math.sqrt(max(0, t2))
print(answer) | MathQA_Geometry |
Geometry | geometry | how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches ? | 100 | n0 = 11.0
n1 = 13.0
n2 = 6.5
n3 = 11.0
t0 = n0 * n1 # area of rectangle
t1 = n0 * n2 # area of rectangle
t2 = t0 * 2.0
t3 = t1 * 2.0
t4 = t2 - t3
t5 = t4 / t0
answer = t5 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | if g is the smallest positive integer such that 3150 multiplied by g is the square of an integer , then g must be | 14 | n0 = 3150.0
t0 = 2.0 + 3.0
t1 = n0 / 2.0
t2 = t1 / t0
t3 = t2 / t0
t4 = t3 / 3.0
t5 = t4 / 3.0
answer = t5 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the width of a rectangular hall is ½ of its length . if the area of the hall is 288 sq . m , what is the difference between its length and breadth ? | 12 | import math
n0 = 288.0
t0 = 1.0 / 2.0
t1 = n0 / t0
t2 = math.sqrt(max(0, t1))
answer = t2 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface . | 60 | import math
n0 = 10.0
n1 = 8.0
t0 = n0**min(2.0, 5)
t1 = n1**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
answer = n0 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | 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 = n0 + n1
t1 = n0 * n1
t2 = t1 * 2.0
t3 = t0 * 2.0
t4 = t2 / t3
answer = t4 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a cube of edge 12 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ? | 5.76 | n0 = 12.0
n1 = 20.0
n2 = 15.0
t0 = n1 * n2
t1 = n0**3
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5 . the smaller side of the rectangle is : | 59.97586 | import math
n0 = 42.0
n1 = 6.0
n2 = 5.0
t0 = n1 + n2
t1 = 2 * math.pi * n0
t2 = t0 * 2.0
t3 = t1 / t2
answer = n2 * t3
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 | 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 fit in the crate ? | 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 | if each side of a right triangle is increased by 10 % and the base ( b ) is half of the height , find the percentage change in its area ? | 21 | n0 = 10.0
t0 = n0 + 100.0
t1 = t0 / 100.0
t2 = t1**min(2.0, 5)
t3 = t2 - 1.0
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | 32 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ? | 8 | n0 = 32.0
answer = n0 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters . if the carpet squares cost $ 24 apiece , what is the total cost for the number of carpet squares needed to cover the floor ? | 576 | n0 = 24.0
n1 = 64.0
n2 = 8.0
n3 = 8.0
n4 = 24.0
answer = n0 * n0
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a cube is 12 m , find the lateral surface area ? | 516 | n0 = 12.0
t0 = 10.0 * 4.0
t1 = t0 + 3.0
answer = n0 * t1 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ? | 26 | n0 = 20.0
n1 = 60.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | if the volume of a cube is x ^ 3 cubic units , what is the number of square units in the surface area of the cube ? | 6 | n0 = 3.0
t0 = 2.0 * 3.0
t1 = 1.0 * 1.0
answer = t0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a metallic sheet is of rectangular shape with dimensions 48 m x 38 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is : | 5,632 | n0 = 48.0
n1 = 38.0
n2 = 8.0
n3 = 3.0
t0 = n2 * 2.0
t1 = n0 - t0
t2 = n1 - t0
answer = n2 * t1 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is | 90.25 | n0 = 10.0
t0 = n0 - 0.25
t1 = t0 - 0.25
answer = t1**min(2.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 84 ounces of this substance ? | 36 | n0 = 48.0
n1 = 112.0
n2 = 84.0
t0 = n0 / n1
answer = n2 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ? | 72 | n0 = 12.0
n1 = 6.0
answer = n0 * n1 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a certain farmer pays $ 60 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre ) | 600 | n0 = 60.0
n1 = 360.0
n2 = 1210.0
n3 = 43560.0
n4 = 1.0
t0 = n1 * n2
t1 = t0 / 10.0
t2 = t0 / t1
answer = n0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of a parallelogram with base 26 cm and height 14 cm ? | 364 | n0 = 26.0
n1 = 14.0
answer = n0 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | thin rectangular slab of potato was cut into two pieces for an osmosis lab . one piece is 50 mm greater than the other . if the original uncut slab is 600 mm , what is the length of the other piece of the potato after it is cut . | 275 | n0 = 50.0
n1 = 600.0
t0 = n1 - n0
answer = t0 / 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 | the area of a square is 144 m ² . find its perimeter . | 48 | import math
n0 = 144.0
t0 = math.sqrt(max(0, n0))
answer = 4 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 14 inches on a side and costs $ 10 , and a large pizza that measures 21 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ? | 49 | n0 = 14.0
n1 = 10.0
n2 = 21.0
n3 = 20.0
n4 = 30.0
t0 = n2**min(2.0, 5)
t1 = n0**min(2.0, 5)
t2 = t1 + t0
t3 = t0 * 3.0
t4 = t2 + t2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of square field whose side of length 17 m ? | 289 | n0 = 17.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 30 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ? | 30 | n0 = 1.0
n1 = 1.0
n2 = 30.0
n3 = 1.0
n4 = 2.0
t0 = n0 + n4
t1 = n0 / t0
t2 = n2 * t1
answer = t0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular grass field is 75 m * 55 m , it has a path of 2.8 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ? | 1,518.72 | n0 = 75.0
n1 = 55.0
n2 = 2.8
n3 = 2.0
t0 = n2 * n3
t1 = n0 * n1 # area of rectangle
t2 = n0 + t0
t3 = n1 + t0
t4 = t2 * t3 # area of rectangle
t5 = t4 - t1
answer = n3 * t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is increased by 45 % and its breadth is decreased by 20 % . what is the effect on its area ? | 11,600 | n0 = 45.0
n1 = 20.0
t0 = n0 + 100.0
t1 = 100.0 - n1
answer = t0 * t1
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 | 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ? | 150 | import math
n0 = 30.0
n1 = 67.5
t0 = n1 / n0
t1 = math.sqrt(max(0, t0))
answer = t1 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ? | 5.656854 | import math
n0 = 8.0
n1 = 8.0
n2 = 2.0
t0 = math.sqrt(max(0, n2))
t1 = n0 * t0
answer = t1 / n2
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 | the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the width of this rectangle . | 15 | import math
n0 = 300.0
n1 = 70.0
t0 = n1 / 2.0
t1 = n0 * 4.0
t2 = t0 * t0
t3 = t2 - t1
t4 = math.sqrt(max(0, t3))
t5 = t0 - t4
answer = t5 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ? | 72 | n0 = 0.0
n1 = 4.5
n2 = 8.0
n3 = 0.0
n4 = 0.0
n5 = 4.5
n6 = 8.0
n7 = 0.0
t0 = n2 * 2.0
t1 = n1 * 2.0
answer = t0 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonals of a rhombus are 14 cm and 18 cm . find its area ? | 126 | n0 = 14.0
n1 = 18.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular swimming pool is 10 feet by 12 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 360 square feet . what is the width of the deck ? | 4 | import math
n0 = 10.0
n1 = 12.0
n2 = 360.0
t0 = n0 * n1 # area of rectangle
t1 = n1 - 1.0
t2 = t1**min(2.0, 5)
t3 = n2 - t0
t4 = t2 + t3
t5 = math.sqrt(max(0, t4))
t6 = t5 - t1
answer = t6 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintainthe original area ? | 28.205128 | n0 = 22.0
t0 = 100.0 - n0
t1 = t0 / 100.0
t2 = 1.0 - t1
t3 = t2 / t1
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ? | 135 | n0 = 19.0
t0 = n0 - 1.0
t1 = t0 - 3.0
t2 = t0 * t1
answer = t2 / 2.0
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 r 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 | 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 length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is : | 30 | n0 = 5.0
n1 = 750.0
n2 = 2.0
t0 = n1 / n0
answer = t0 / n0
print(answer) | MathQA_Geometry |
Geometry | geometry | a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 211 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ? | 11,236 | n0 = 1.0
n1 = 211.0
t0 = n1 - n0
t1 = t0 / 2.0
t2 = n0 + t1
answer = t2**min(2.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonals of a rhombus are 15 cm and 17 cm . find its area ? | 127.5 | n0 = 15.0
n1 = 17.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 440 sq . feet , how many feet of fencing will be required ? | 64 | n0 = 20.0
n1 = 440.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is : | 125 | import math
n0 = 50.0
t0 = n0 / 100.0
t1 = 4 * math.pi * 1.0**2
t2 = t0 + 1.0
t3 = 4 * math.pi * t2**2
t4 = t3 - t1
t5 = t4 / t1
answer = t5 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level . | 11.25 | n0 = 15.0
n1 = 20.0
n2 = 15.0
t0 = n0 * n1
t1 = n0**3
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | in measuring the sides of a rectangle , one side is taken 9 % in excess , and the other 8 % in deficit . find the error percent in the area calculated from these measurements . | 0.28 | n0 = 9.0
n1 = 8.0
t0 = n0 * n1
t1 = n0 - n1
t2 = t0 / 100.0
answer = t1 - t2
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 | 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 50 cm , find the sum of the perimeters of all the triangles . | 300 | n0 = 2.0
n1 = 1.0
n2 = 3.0
n3 = 2.0
n4 = 1.0
n5 = 50.0
t0 = n5 + n5 + n5 # perimeter of a triangle
answer = t0 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ? | 160 | n0 = 39.0
n1 = 32.0
n2 = 10.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of an isosceles right triangle is 12 + 12 sq rt 2 . what is the length of the hypotenuse of the triangle ? | 8.485281 | import math
n0 = 12.0
n1 = 12.0
n2 = 2.0
t0 = math.sqrt(max(0, n2))
t1 = n0 * t0
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a equilateral triangle having one side 5 m . in this triangle there is a square of side 2 m . calculate the percentage of area outside square in that triangle . | 63.049583 | import math
n0 = 5.0
n1 = 2.0
t0 = n0**min(2.0, 5)
t1 = math.sqrt(max(0, 3.0))
t2 = n1**2
t3 = t1 / 4.0
t4 = t3 * t0
t5 = t4 - t2
t6 = t5 / t4
answer = t6 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 4 inches tall . how tall are the sculpture andbase together ? | 3.166667 | n0 = 2.0
n1 = 10.0
n2 = 4.0
t0 = n0 + n1
t1 = n0 * t0
t2 = t1 + 10.0
t3 = n2 + t2
answer = t3 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the perimeter and area of a square of side 9 cm . | 81 | n0 = 9.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ? | 88 | n0 = 0.0
n1 = 5.5
n2 = 8.0
n3 = 0.0
n4 = 0.0
n5 = 5.5
n6 = 8.0
n7 = 0.0
t0 = n2 * 2.0
t1 = n1 * 2.0
answer = t0 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a circle is increased by 300 % . by what percent has the diameter of the circle increased ? | 100 | n0 = 300.0
t0 = 2.0 / 2.0
answer = t0 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of the rectangular field is double its width . inside the field there is square shaped pond 5 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ? | 20 | import math
n0 = 5.0
n1 = 1.0
n2 = 8.0
t0 = 1 / 2.0
t1 = n0**2
t2 = n2 * t1
t3 = t2 / t0
answer = math.sqrt(max(0, t3))
print(answer) | MathQA_Geometry |
Geometry | geometry | in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 20 feet between each tree . how many trees can be planted if the road is 148 feet long ? | 8 | n0 = 20.0
n1 = 148.0
t0 = n0 + 1.0
t1 = n1 - 1.0
t2 = t1 / t0
answer = t2 + 1.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 384 meters , what is the width of the field ? | 80 | n0 = 7.0
n1 = 5.0
n2 = 384.0
t0 = n0 / n1
t1 = t0 + t0
t2 = t1 + 2.0
answer = n2 / t2
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 | a crate measures 7 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 fit in the crate ? | 7 | n0 = 7.0
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 semicircle has a radius of 14 . what is the approximate perimeter of the semicircle ? | 71.982297 | import math
n0 = 14.0
t0 = 2 * math.pi * n0
t1 = n0 * 2.0
t2 = t0 / 2.0
answer = t2 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is | 42.06196 | n0 = 7.0
n1 = 7.0
t0 = n0 * 2.0
t1 = n0**min(2.0, 5)
t2 = t1 * 3.141592653589793
t3 = t0**min(2.0, 5)
answer = t3 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the ratio of the areas of two squares , one having double its diagonal then the other is : | 4 | t0 = 1 / 2.0
t1 = t0 * 4.0
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | if abc is a quarter circle and a smaller circle is inscribed in it ; if radius of quarter circle is 1.414 units . find the radius of smaller circle | 0.586 | n0 = 1.414
answer = 2.0 - n0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the surface area of a 8 cm x 6 cm x 2 cm brick . | 152 | n0 = 8.0
n1 = 6.0
n2 = 2.0
answer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism
print(answer) | MathQA_Geometry |
Geometry | geometry | in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the error percent in the area calculated from these measurements . | 0.8 | n0 = 5.0
n1 = 4.0
t0 = n0 * n1
t1 = n0 - n1
t2 = t0 / 100.0
answer = t1 - t2
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 | the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ? | 82 | n0 = 40.0
n1 = 30.0
t0 = n0 / 100.0
t1 = n1 / 100.0
t2 = t0 + 1.0
t3 = t1 + 1.0
t4 = t2 * t3
t5 = t4 - 1.0
answer = t5 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | while visiting a small town in the united states , i lost my overcoat in a bus . when i reported the matter to the bus company i was asked the number of the bus . though i did not remember the exact number i did remember that the bus number bad a certain peculiarity about it . the number plate showed the bus number as a perfect square and also if the plate was turned upside down . ? the number would still be a perfect square — of course it was not ? i came to know from the bus company they had only 5 100 buses numbered from 1 to 500 . from this i was able to deduce the bus number . can you tell what was the other number . | 196 | n0 = 5.0
n1 = 100.0
n2 = 1.0
n3 = 500.0
t0 = n1 - 4.0
answer = t0 + 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long . over how much area of the field can it graze ? | 380.132711 | n0 = 45.0
n1 = 25.0
n2 = 22.0
t0 = n2**min(2.0, 5)
t1 = t0 * 3.141592653589793
answer = t1 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ? | 21 | n0 = 3.78
n1 = 5.25
t0 = n0 * 100.0
t1 = t0 / 3.0
t2 = t1 / 3.0
t3 = t2 / 3.0
t4 = t3 / 2.0
answer = t4 * 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | four equal circles are described about the four corners of a square so that each touches two of the others . if a side of the square is 14 cm , then the area enclosed between the circumferences of the circles is : | 42.06196 | import math
n0 = 14.0
t0 = n0 / 2.0
t1 = n0**2
t2 = math.pi * t0**2
answer = t1 - t2
print(answer) | MathQA_Geometry |
Math Dataset for elementary school grade
This repository is dedicated to compiling a comprehensive and balanced dataset tailored to match the mathematics curriculum for 10-year-olds. Our goal is to provide a robust resource that supports the development and evaluation of educational tools like chatbots, which can effectively answer math questions tailored to elementary students.
For more info, please visit our GitHub.
Methodology
We followed a methodical approach to construct this dataset:
Classification of Math Questions: We categorized questions to allow for targeted educational interventions and specialized solution techniques.
Search for Suitable Datasets: We identified datasets for each category, ensuring they align with the learning level and content requirements of elementary school math.
Compilation and Sampling: We combined and randomly sampled from exisitng datasets to create a diverse collection that accurately mirrors the types of math challenges faced by 10-year-olds.
Categorization
Our dataset categorizes mathematical questions into three groups:
- Arithmetic: Includes basic calculations, measurement conversions, and more. (E.g. "What is 1.20m in mm?" or "What is 12+8?")
- Word Problems: Engages students with real-world scenarios requiring mathematical solutions. (E.g. "If you split 50$ equally among 5 people, how much does each get?")
- Geometry: Focuses on shape, space, and measurement problems suitable for young learners. (E.g. "What is the volume of a sphere with radius 6 cm?")
These categories where inspired by Ahn et al., 2024.
Dataset Selection Criteria
We adhered to rigorous criteria to ensure the dataset's relevance and quality:
- Language: English-only to maintain consistency across data.
- Educational Level: Suitable for elementary school math levels.
- Content Type: Focused exclusively on text-based datasets, avoiding any that include pictures or additional multimedia sources to ensure straightforward analysis.
- Single Float Answer: The answer to each question is a single float value. This ensures easy evaluation.
Dataset Overview
Format
The dataset is a collection of .json
objects. Each object has the following format:
{
"category": "Arithmetic | Word Problems | Gemoetry",
"subcategory": "<divided category further>",
"question": "<question>",
"answer": "<answer as float>",
"reasoning": "(optional) <can be an equation, python program, etc.>",
"source": "<source dataset name>"
}
Example Entry (from the SVAMP dataset):
{
"category": "Word Problem",
"subcategory": "challenge",
"question": "Dan had $ 3 left with him after he bought a candy bar. If he had $ 4 at the start, how much did the candy bar cost?",
"answer": 1.0,
"reasoning": "( 4.0 - 3.0 )",
"source": "SVAMP"
}
Directory Structure & Data Management
The datasets are versioned into two types for each category:
<category>_1000.csv/json
: A balanced sample of 1000 items, perfect for in-depth testing.<category>_100.csv/json
: A smaller sample of 100 items, designed for quick assessments.
Translation to German
We translated the datasets to german (using the DeepL API). See our GitHub for the dataset and more info.
Oerview of the different dataset versions
This table gives an overview of the different dataset versions.
Section | Name | Number of subcategories | Size |
---|---|---|---|
I. Arithmetic | arithmetic_complete |
14 | 7,731,654 |
arithmetic_1000 |
14 | 1,000 | |
arithmetic_100 |
14 | 100 | |
II. Word Problems | wordProblems_complete |
3 | 1,995 |
wordProblems_1000 |
3 | 1,000 | |
wordProblems_100 |
3 | 100 | |
III. Geometry | geometry_complete |
1 | 1,698 |
geometry_1000 |
1 | 1,000 | |
geometry_100 |
1 | 100 |
Exploring the Dataset
A nice overview of all available datasets in the mathematical domain can be found in Lu et al, 2023 and in Ahn et al., 2024.
In constructing this dataset, we made a concerted effort to include a comprehensive range of datasets that are best suited for the educational level and cognitive abilities of 10-year-olds. While we don't provide extensive details on the selection process for each dataset, our overarching goal was to incorporate as many relevant and suitable datasets as possible.
I. Arithmetic |
|||
---|---|---|---|
Source | Subcategory | Size | Example |
Math-401 | arithmetic_mixed |
71 | log 10(797)= |
Mathematics Dataset (Google Deepmin) | add_or_sub |
71 | What is -6.5 + -1.5? |
add_sub_multiple |
71 | Calculate -4 + 0 - ((-3 - -1) + 7). | |
conversion |
71 | What is three eighths of a kilogram in grams? | |
div |
71 | Calculate -238 divided by -3. | |
div_remainder |
73 | What is the remainder when 255 is divided by 20? | |
gcd |
72 | What is the highest common divisor of 75 and 390? | |
lcm |
72 | Calculate the lowest common multiple of 1355 and 80. | |
mul |
72 | Multiply -0.0756 and 0.14. | |
mul_div_multiple |
71 | Evaluate 2/(-6)*(-120)/(-80). | |
place_value |
71 | What is the tens digit of 5546? | |
round_number |
71 | Round 4117.6 to the nearest 10. | |
sequence_next_term |
72 | What comes next: -75, -80, -85, -90? | |
time |
71 | How many minutes are there between 1:03 PM and 9:11 PM? | |
II. Word Problems |
|||
Source | Subcategory | Size | Example |
SVAMP | challenge |
334 | At the arcade Edward won 9 tickets. If he spent 4 tickets on a beanie and later won 4 more tickets, how many would he have? |
AddSub | add_sub |
333 | Tim has 44 books. Sam has 52 books. How many books do they have together? |
MultiArith | multi_step |
333 | Roger had 25 books. If he sold 21 of them and used the money he earned to buy 30 new books, how many books would Roger have? |
III. Geometry |
|||
Source | Subcategory | Size | Example |
MathQA Geometry | geometry |
1000 | Find the surface area of a 8 cm x 6 cm x 2 cm brick |
References
Overview of existing datasets in the mathematical domain:
- P. Lu, L. Qiu, W. Yu, S. Welleck, and K.-W. Chang, “A Survey of Deep Learning for Mathematical Reasoning.” arXiv, Jun. 21, 2023. Accessed: May 02, 2024. [Online]. Available: http://arxiv.org/abs/2212.10535
- J. Ahn, R. Verma, R. Lou, D. Liu, R. Zhang, and W. Yin, “Large Language Models for Mathematical Reasoning: Progresses and Challenges.” arXiv, Apr. 05, 2024. doi: 10.48550/arXiv.2402.00157.
- W. Liu et al., “Mathematical Language Models: A Survey.” arXiv, Feb. 23, 2024. Accessed: May 02, 2024. [Online]. Available: http://arxiv.org/abs/2312.07622
References for the used datasets we sampled from:
- Math-401: W. Liu et al., “Mathematical Language Models: A Survey.” arXiv, Feb. 23, 2024. Accessed: May 02, 2024. [Online]. Available: http://arxiv.org/abs/2312.07622
- Mathematics Dataset: D. Saxton, E. Grefenstette, F. Hill, and P. Kohli, “Analysing Mathematical Reasoning Abilities of Neural Models.” arXiv, Apr. 02, 2019. doi: 10.48550/arXiv.1904.01557.
- SVAMP: A. Patel, S. Bhattamishra, and N. Goyal, “Are NLP Models really able to Solve Simple Math Word Problems?” arXiv, Apr. 15, 2021. doi: 10.48550/arXiv.2103.07191.
- AddSub: M. J. Hosseini, H. Hajishirzi, O. Etzioni, and N. Kushman, “Learning to Solve Arithmetic Word Problems with Verb Categorization,” in Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), A. Moschitti, B. Pang, and W. Daelemans, Eds., Doha, Qatar: Association for Computational Linguistics, Oct. 2014, pp. 523–533. doi: 10.3115/v1/D14-1058.
- MultiArith: S. Roy and D. Roth, “Solving General Arithmetic Word Problems.” arXiv, Aug. 20, 2016. doi: 10.48550/arXiv.1608.01413.
- MathQA Geometry: A. Amini, S. Gabriel, S. Lin, R. Koncel-Kedziorski, Y. Choi, and H. Hajishirzi, “MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms,” in Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), J. Burstein, C. Doran, and T. Solorio, Eds., Minneapolis, Minnesota: Association for Computational Linguistics, Jun. 2019, pp. 2357–2367. doi: 10.18653/v1/N19-1245.
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