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
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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