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 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 | the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 55 , then how long is the base of isosceles triangle ? | 15 | n0 = 60.0
n1 = 55.0
t0 = n0 / 3.0
t1 = n1 - t0
answer = t1 - t0
print(answer) | MathQA_Geometry |
Geometry | geometry | rectangular tile each of size 25 cm by 16 cm must be laid horizontally on a rectangular floor of size 180 cm by 120 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of f... | 54 | n0 = 25.0
n1 = 16.0
n2 = 180.0
n3 = 120.0
t0 = n2 * n3
t1 = n0 * n1
answer = t0 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ? | 24 | n0 = 8.0
n1 = 8.0
n2 = 1.0
n3 = 8.0
t0 = n2**(1 / 3)
t1 = n0**(1 / 3)
t2 = 6 * t0**2 # surface of a cube
t3 = 6 * t1**2 # surface of a cube
t4 = n0 * t2
answer = t4 - t3
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 v 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 | by combining number of small cubes , a larger cube is produced . the ratio between volume of larger cube and small cube is 1000 : 8 then how many small cubes are required to produce a larger cube ? | 125 | n0 = 1000.0
n1 = 8.0
answer = n0 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | approximately how many cubic feet of water are needed to fill a circular swimming pool that is 80 feet across and 10 feet deep ? | 50,265.482457 | import math
n0 = 80.0
n1 = 10.0
t0 = n0 / 2.0
answer = math.pi * t0**2 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ? | 2.828427 | import math
n0 = 4.0
n1 = 4.0
n2 = 2.0
t0 = math.sqrt(max(0, n2))
t1 = n0 * t0
answer = t1 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | on dividing a number by 5 , we get 3 as remainder . what will the remainder when the square of the this number is divided by 5 ? | 4 | import math
n0 = 5.0
n1 = 3.0
n2 = 5.0
t0 = n1**min(2.0, 5)
t1 = t0 / n0
t2 = math.floor(t1)
t3 = t1 - t2
answer = n0 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | the sides of a square region , measured to the nearest centimeter , are 7 centimeters long . the least possible value of the actual area of the square region is | 42.25 | n0 = 7.0
t0 = n0 - 0.25
t1 = t0 - 0.25
answer = t1**min(2.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | a wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule , whose length and breadth are in the ratio of 6 : 5 . what is the area of the rectangle ? | 29.975865 | import math
n0 = 3.5
n1 = 6.0
n2 = 5.0
t0 = n1 + n2
t1 = 2 * math.pi * n0
t2 = t0 * 2.0
t3 = t1 / t2
t4 = n1 * t3
t5 = n2 * t3
answer = t4 * t5 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of a cube is 729 cc . find its surface . | 486 | n0 = 729.0
t0 = n0**(1 / 3)
answer = 6 * t0**2 # surface of a cube
print(answer) | MathQA_Geometry |
Geometry | geometry | a park square in shape has a 3 metre wide road inside it running along its sides . the area occupied by the road is 1764 square metres . what is the perimeter along the outer edge of the road ? | 600 | n0 = 3.0
n1 = 1764.0
t0 = n0 * 2.0
t1 = t0 * 2.0
t2 = t0**min(2.0, 5)
t3 = n1 + t2
t4 = t3 / t1
answer = t4 * 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ? | 9 | n0 = 18.0
answer = n0 / 2.0
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 | a rectangular grass field is 65 m * 55 m , it has a path of 2.5 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 ? | 1,250 | n0 = 65.0
n1 = 55.0
n2 = 2.5
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 | three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ? | 32 | n0 = 280.0
n1 = 180.0
n2 = 36.0
t0 = n0 - n1
t1 = t0 - n2
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of square field whose side of length 16 m ? | 256 | n0 = 16.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | abcd is a square where ab = â ˆ š 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd . | 2,002 | n0 = 4004.0
answer = n0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the p... | 3 | n0 = 2.0
n1 = 4.0
n2 = 180.0
n3 = 1.0
n4 = 6.0
n5 = 190.0
n6 = 195.0
t0 = -n0
t1 = n5 * t0
t2 = n4 * t0
t3 = n2 + t1
t4 = n1 + t2
t5 = t3 / t4
t6 = n4 * t5
t7 = n5 - t6
t8 = t5 + t7
answer = n6 / t8
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of a parallelogram with base 36 cm and height 24 cm ? | 864 | n0 = 36.0
n1 = 24.0
answer = n0 * n1
print(answer) | MathQA_Geometry |
Geometry | geometry | how many internal diagonals does a hexagon ( 6 sided polygon ) have ? | 9 | n0 = 6.0
t0 = n0 - 3.0
t1 = n0 * t0
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many... | 10,000 | n0 = 1.0
n1 = 199.0
t0 = 0.25 + 0.25
t1 = n1 / 2.0
t2 = t0 + t1
answer = t2**min(2.0, 5)
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 9 feet between each tree . how many trees can be planted if the road is 151 feet long ? | 16 | n0 = 9.0
n1 = 151.0
t0 = n0 + 1.0
t1 = n1 - 1.0
t2 = t1 / t0
answer = t2 + 1.0
print(answer) | MathQA_Geometry |
Geometry | geometry | abcd is a square aegf is a rectangle . . such that the rectangle shares 25 % of the area of the suare also ae lies on the line ab and ag lies on segment of ad . if the square shares half the area of the rectangle what is the ratio ae : ag ? | 8 | n0 = 25.0
t0 = n0 / 100.0
t1 = 1.0 / 2.0
t2 = 1.0 / t0
answer = t2 / t1
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 256 sq . feet , how many feet of fencing will be required ? | 45.6 | n0 = 20.0
n1 = 256.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | three fifth of the square of a certain number is 126.15 . what is the number ? | 14.5 | import math
n0 = 126.15
t0 = 1.0 + 4.0
t1 = 3.0 / t0
t2 = n0 / t1
answer = math.sqrt(max(0, t2))
print(answer) | MathQA_Geometry |
Geometry | geometry | one side of a rectangular field is 4 m and its length along diagonal is 5 m . what is the area of the field ? | 12 | import math
n0 = 4.0
n1 = 5.0
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 parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 16 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 ) ? | 28.274334 | import math
n0 = 20.0
n1 = 16.0
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 circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ? | 6 | import math
n0 = 6.0
t0 = n0 * n0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | abcd is a square where ab = â ˆ š 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd . | 2,016 | n0 = 4032.0
answer = n0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ? | 4.8 | n0 = 12.0
n1 = 8.0
t0 = n0 * n1
t1 = t0 / 2.0
answer = t1 / 10.0
print(answer) | MathQA_Geometry |
Geometry | geometry | of the two square fields , the area of the one is 1 hectare , while anothe one is broader by 1 % . there differences in area is : | 201 | import math
n0 = 1.0
n1 = 1.0
t0 = 10.0 * 1000.0
t1 = math.sqrt(max(0, t0))
t2 = n0 + t1
t3 = t2**2
answer = t3 - t0
print(answer) | MathQA_Geometry |
Geometry | geometry | there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure q in inches of the width of the ... | 10 | n0 = 1.0
n1 = 128.0
n2 = 128.0
t0 = 1 / 3.0
t1 = n0 * 2.0
t2 = n0 * t1
t3 = n1 / t2
t4 = t3**min(t0, 5)
t5 = t1 * t4
answer = t5 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of the square , one of whose diagonals is 3.8 m long ? | 7.22 | n0 = 3.8
t0 = 1.0 / 2.0
t1 = n0 * n0
answer = t0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be | 10 | n0 = 4410.0
t0 = 2.0 + 3.0
answer = t0 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is increased by 40 % while its width is halved . what is the % change in area ? | 30 | n0 = 40.0
t0 = n0 / 100.0
t1 = 1.0 / 2.0
t2 = t0 + 1.0
t3 = t2 * t1
t4 = 1.0 - t3
answer = t4 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | rectangular tile each of size 45 cm by 50 cm must be laid horizontally on a rectangular floor of size 250 cm by 180 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of f... | 20 | n0 = 45.0
n1 = 50.0
n2 = 250.0
n3 = 180.0
t0 = n2 * n3
t1 = n0 * n1
answer = t0 / t1
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 | 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 wate... | 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 | three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ? | 40 | n0 = 300.0
n1 = 180.0
n2 = 40.0
t0 = n0 - n1
t1 = t0 - n2
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ? | 3 | n0 = 2.0
n1 = 4.0
n2 = 200.0
n3 = 1.0
n4 = 6.0
n5 = 220.0
n6 = 210.0
t0 = n2 / 2.0
t1 = n5 - t0
t2 = t1 / n1
t3 = n4 * t2
t4 = n5 - t3
t5 = t2 + t4
answer = n6 / t5
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 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of wate... | 50 | n0 = 1.0
n1 = 1.0
n2 = 50.0
n3 = 1.0
n4 = 3.0
t0 = n0 + n4
t1 = n0 / t0
t2 = n2 * t1
answer = t0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a rhombus is 25 m and length of one of its diagonals is 10 m . the area of the rhombus is ? | 244.948974 | import math
n0 = 25.0
n1 = 10.0
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 | 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 gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 191 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many... | 9,216 | n0 = 1.0
n1 = 191.0
t0 = 0.25 + 0.25
t1 = n1 / 2.0
t2 = t0 + t1
answer = t2**min(2.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | a metallic sheet is of rectangular shape with dimensions 40 m x 30 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 cube ) is : | 2,688 | n0 = 40.0
n1 = 30.0
n2 = 8.0
t0 = n2 * 2.0
t1 = n0 - t0
t2 = n1 - t0
answer = n2 * t1 * t2
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 | an isosceles triangle with sides 13 13 10 and there is a circle inscribed it . find the radius of circle ? | 3.333333 | import math
n0 = 13.0
n1 = 13.0
n2 = 10.0
t0 = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n0 + n2) / 2, n0, n0, n2) # Heron's formula
t1 = n0 + n0 + n2 # perimeter of a triangle
t2 = t0 * 2.0
answer = t2 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the floor of a rectangular room is 20 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 : | 144 | n0 = 20.0
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 | the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ? | 44 | n0 = 5.0
n1 = 8.0
n2 = 14.0
answer = 4.0 * (n2 + n1) / 2 # quadrilateral area
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ? | 1.5 | n0 = 1.5
t0 = n0 / n0
answer = n0 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a right triangle aec has to be constructed in the xy - plane so that the right angle is at a and ae is parallel to x axis . the coordinates of a , e and c are integers and satisfy the inequalities - 1 ≤ x ≤ 7 and 1 ≤ y ≤ 7 . how many different triangles can be constructed with these properties ? | 3,024 | import math
n0 = 1.0
n1 = 7.0
n2 = 1.0
n3 = 7.0
t0 = math.factorial(min(15, int(n1)))
t1 = n1 * 2.0
t2 = n1 - n0
t3 = t2 * 4.0
t4 = t3 * t2
t5 = t4 * t1
answer = t0 - t5
print(answer) | MathQA_Geometry |
Geometry | geometry | if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a sixth of a circle ? | 6,000 | n0 = 1.0
n1 = 1.0
t0 = 2.0 + 4.0
t1 = 3600.0 / 10.0
t2 = n0 / t0
t3 = t1 * 100.0
answer = t2 * t3
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 | a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ? | 12 | n0 = 9.0
n1 = 3.0
n2 = 2.0
t0 = n1 + 4.0
t1 = n0 * n1
t2 = n2 * 4.0
t3 = t1 - t0
answer = t3 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a circular mat with radius 10 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ? | 0.545415 | import math
n0 = 10.0
n1 = 24.0
t0 = math.pi * n0**2
t1 = n1**2
answer = t0 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the total surface area in square meters of a rectangular solid whose length is 5 meters , width is 4 meters , and depth is 1 meters ? | 58 | n0 = 5.0
n1 = 4.0
n2 = 1.0
answer = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism
print(answer) | MathQA_Geometry |
Geometry | geometry | if a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ? | 30 | import math
n0 = 2.0
n1 = 3.0
n2 = 4.0
n3 = 3.0
n4 = 28.0
n5 = 7.0
t0 = n0 + n4
t1 = n1 + n5
t2 = n0 + n2
t3 = n4 - n2
t4 = t0**min(2.0, 5)
t5 = t1**min(2.0, 5)
t6 = t3**min(2.0, 5)
t7 = t2**min(2.0, 5)
t8 = t4 + t5
t9 = t6 + t5
t10 = math.sqrt(max(0, t7))
t11 = math.sqrt(max(0, t8))
t12 = math.sqrt(max(0, t9))
answer ... | MathQA_Geometry |
Geometry | geometry | a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 2 , 4 ) . what is the smallest possible area of that circle ? | 15.25 | import math
n0 = 3.0
n1 = 2.0
n2 = 2.0
n3 = 4.0
t0 = n0 + n2
t1 = n1 + n3
t2 = t0 * t0
t3 = t1 * t1
t4 = t2 + t3
t5 = math.sqrt(max(0, t4))
t6 = t5 / n1
answer = t6**2
print(answer) | MathQA_Geometry |
Geometry | geometry | a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ? | 102.831853 | import math
n0 = 20.0
t0 = 2 * math.pi * n0
t1 = n0 * 2.0
t2 = t0 / 2.0
answer = t2 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ? | 75 | n0 = 37.0
n1 = 64.0
n2 = 19.0
n3 = 27.0
t0 = 1.0 / 3.0
t1 = n1**min(t0, 5)
t2 = n3**min(t0, 5)
t3 = t1 * t2
t4 = t3 + t1
t5 = t4 - t1
t6 = t1 + t5
t7 = t6 - t1
t8 = t7 / t6
answer = t8 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 22 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ? | 103 | n0 = 22.0
t0 = 1.0 + 3.0
t1 = t0 + 1.0
t2 = t1**min(3.0, 5)
answer = t2 - n0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ? | 7 | import math
n0 = 1225.0
n1 = 2.0
n2 = 20.0
t0 = math.sqrt(max(0, n0))
t1 = t0 * 4.0
answer = t1 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | two circular frames are kept one above the other . frame x has a diameter of 16 cm and frame y has a diameter of 12 cm . what fraction of the surface of frame x is not covered by frame y ? | 0.4375 | import math
n0 = 16.0
n1 = 12.0
t0 = n0 / 2.0
t1 = n1 / 2.0
t2 = math.pi * t0**2
t3 = math.pi * t1**2
t4 = t2 - t3
answer = t4 / t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side | 6,000 | n0 = 50.0
n1 = 1.0
n2 = 20.0
n3 = 20.0
t0 = 6 * n3**2 # surface of a cube
t1 = t0 / n2
answer = n0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 7.5 ) , ( 8 , 0 ) , ( 0 , - 7.5 ) , ( - 8 , 0 ) ? | 120 | n0 = 0.0
n1 = 7.5
n2 = 8.0
n3 = 0.0
n4 = 0.0
n5 = 7.5
n6 = 8.0
n7 = 0.0
t0 = n2 * 2.0
t1 = n1 * 2.0
answer = t0 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | 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 12 feet between each tree . how many trees can be planted if the road is 157 feet long ? | 13 | n0 = 12.0
n1 = 157.0
t0 = n0 + 1.0
t1 = n1 - 1.0
t2 = t1 / t0
answer = t2 + 1.0
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 . 7 per metre approximately | 10,398.36907 | import math
n0 = 17.56
n1 = 7.0
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 | the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 18 - inch screen would be how many square inches greater than the area of a square 16 - inch screen ? | 34 | n0 = 18.0
n1 = 16.0
t0 = n0**min(2.0, 5)
t1 = n1**min(2.0, 5)
t2 = t0 - t1
answer = t2 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ? | 36 | import math
n0 = 9.0
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 | 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 | a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ? | 27 | n0 = 3.0
n1 = 27.0
n2 = 3.0
t0 = n1 / n0
answer = n2 * t0
print(answer) | MathQA_Geometry |
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 7 m , the volume of the box ( in m 3 ) is : | 5,236 | n0 = 48.0
n1 = 36.0
n2 = 7.0
n3 = 3.0
t0 = n2 * 2.0
t1 = n0 - t0
t2 = n1 - t0
answer = n2 * t1 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | sides of a triangle are 13 cm . 14 cm . and 15 cm . respectively . calculate the area of triangle . | 84 | import math
n0 = 13.0
n1 = 14.0
n2 = 15.0
answer = (lambda s, a, b, c: math.sqrt(max(0, s * (s - a) * (s - b) * (s - c))))((n0 + n1 + n2) / 2, n0, n1, n2) # Heron's formula
print(answer) | MathQA_Geometry |
Geometry | geometry | the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle sho... | 72 | n0 = 2.0
n1 = 3.0
t0 = n0 + n1
t1 = 1.0 / n1
t2 = n1 / t0
t3 = t2 * 360.0
answer = t1 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ? | 384 | n0 = 4.0
n1 = 4.0
n2 = 4.0
n3 = 10.0
n4 = 12.0
n5 = 16.0
t0 = n4 * n5
t1 = n0 * 2.0
t2 = n3 - t1
answer = t0 * t2
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 | a circular ground whose diameter is 70 metres , has a 2.8 metre - broad garden around it . what is the area of the garden in square metres ? | 640.382247 | import math
n0 = 70.0
n1 = 2.8
t0 = n0 / 2.0
t1 = n1 + t0
t2 = math.pi * t0**2
t3 = math.pi * t1**2
answer = t3 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ? | 15 | n0 = 5.0
n1 = 24.0
n2 = 8.0
t0 = n0 * n1 # area of rectangle
answer = t0 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the ratio g of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ? | 0.6 | t0 = 2.0 * 3.0
t1 = 1.0 * 2.0
t2 = 1.0 * 1.0
t3 = t1 * 2.0
t4 = t3 + t2
t5 = t4 * 2.0
answer = t0 / t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface of a cube is 96 sq cm . find its volume ? | 64 | import math
n0 = 96.0
t0 = 2.0 + 4.0
t1 = n0 / t0
t2 = math.sqrt(max(0, t1))
answer = t2**3
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 . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | 5,436 | n0 = 25.0
n1 = 15.0
n2 = 12.0
n3 = 6.0
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 radius of a cone is 10 m , height 21 m . the volume of the cone is : | 2,199.114858 | import math
n0 = 10.0
n1 = 21.0
answer = math.pi * n0**2 * n1 / 3
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ? | 18 | import math
n0 = 972.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
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 | a box measuring 49 inches long by 42 inches wide by 14 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 ? | 84 | n0 = 49.0
n1 = 42.0
n2 = 14.0
t0 = n2 / 2.0
t1 = n0 * n1
t2 = n2 * t1
t3 = t0**3
answer = t2 / t3
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a square field is 625 km 2 . how long will it take for a horse to run around at the speed of 25 km / h ? | 4 | import math
n0 = 625.0
n1 = 2.0
n2 = 25.0
t0 = math.sqrt(max(0, n0))
t1 = t0 * 4.0
answer = t1 / n2
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 56 ounces of this substance ? | 24 | n0 = 48.0
n1 = 112.0
n2 = 56.0
t0 = n0 / n1
answer = n2 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is 2 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ? | 50 | n0 = 2.0
n1 = 5.0
t0 = n0 * n1
answer = n1 * t0 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | right triangle pqr is the base of the prism in the figure above . if pq = pr = â ˆ š 5 and the height of the prism is 10 , what is the volume of the prism ? | 25 | import math
n0 = 5.0
n1 = 10.0
t0 = math.sqrt(max(0, n0))
t1 = t0 * t0 / 2
answer = n1 * 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 parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 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 ) ? | 21.991149 | import math
n0 = 18.0
n1 = 10.0
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 | if the height of a cone is increased by 100 % then its volume is increased by ? | 100 | n0 = 100.0
answer = n0 * 1.0 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ? | 44 | n0 = 20.0
t0 = n0 / 100.0
t1 = t0 + 1.0
t2 = t1**min(2.0, 5)
t3 = t2 - 1.0
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ? | 76,800 | n0 = 560.0
n1 = 400.0
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 base of a triangular field is three times its altitude . if the cost of cultivating the field at rs . 24.68 per hectare be rs . 333.18 , find its base and height . | 300 | n0 = 24.68
n1 = 333.18
t0 = n1 / n0
t1 = 3.0 / 2.0
t2 = t0 * 1000.0
t3 = t2 / 3.0
t4 = t3 / 10.0
answer = t4 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a triangle is with base 4.5 m and height 6 m ? | 13.5 | n0 = 4.5
n1 = 6.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle sho... | 198 | n0 = 2.0
n1 = 3.0
n2 = 3.0
n3 = 4.0
t0 = n0 + n1
t1 = 360.0 / t0
t2 = n1 * t1
t3 = n0 * t1
t4 = t3 / 4.0
t5 = n1 * t2
t6 = t5 / n3
answer = t6 + t4
print(answer) | MathQA_Geometry |
Geometry | geometry | if the height of a triangle is decreased by 40 % , land its base is increased by 40 % , what will be the effect on its area ? | 16 | n0 = 40.0
n1 = 40.0
t0 = n0 + 100.0
t1 = 100.0 - n0
t2 = t0 * t1
t3 = t2 / 100.0
answer = 100.0 - t3
print(answer) | MathQA_Geometry |
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