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Geometry | geometry | what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ? | 4,012 | import math
n0 = 289.0
n1 = 59.0
t0 = math.sqrt(max(0, n0))
t1 = 4 * t0
answer = n1 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the length of the rectangle ? | 15 | n0 = 5.0
n1 = 1.0
n2 = 150.0
answer = n2 / 10.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the sides of a rectangle are in the ratio 4 : 3 and its area is 972 sq . m find the perimeter of rectangle | 126 | import math
n0 = 4.0
n1 = 3.0
n2 = 972.0
t0 = n0 * n1
t1 = n2 / t0
t2 = math.sqrt(max(0, t1))
t3 = n0 * t2
t4 = n1 * t2
answer = 2 * (t3 + t4) # perimetere of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ? | 22 | import math
n0 = 6.0
n1 = 5.0
n2 = 120.0
t0 = n0 * 2.0
t1 = n1 * 2.0
t2 = t0 + t1
t3 = t1 * t0
t4 = t2**min(2.0, 5)
t5 = n2 - t3
t6 = t5 * n0
t7 = t6 + t4
t8 = math.sqrt(max(0, t7))
t9 = t2 + t8
answer = t9 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a circular mat with diameter 18 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 ? | 0.375 | n0 = 18.0
n1 = 24.0
t0 = n0 / 2.0
answer = t0 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonals of a rhombus are 12 cm and 15 cm . find its area ? | 90 | n0 = 12.0
n1 = 15.0
answer = n0 * n1 / 2
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 | ratio between length and breath of a rectangle is 25 : 16 . the area of the rectangle is same with a square whose side is 200 . find the breadth and length of the rectangle ? | 160,250 | import math
n0 = 25.0
n1 = 16.0
n2 = 200.0
t0 = n0 * n1
t1 = n2**2
t2 = t1 / t0
t3 = math.sqrt(max(0, t2))
t4 = n1 * t3
t5 = n0 * t3
t6 = t4 * 1000.0
answer = t6 + t5
print(answer) | MathQA_Geometry |
Geometry | geometry | a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube ? | 6 | n0 = 100000.0
t0 = 2.0 + 4.0
answer = t0 / 1.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in measuring the sides of a rectangle , one side is taken 12 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements . | 6.4 | n0 = 12.0
n1 = 5.0
t0 = n0 * n1
t1 = n0 - n1
t2 = t0 / 100.0
answer = t1 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is : | 44 | n0 = 20.0
t0 = n0 + 100.0
t1 = t0 / 100.0
t2 = t1 * t1
t3 = t2 - 1.0
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the circumference and area of radius 8 cm . | 201.06193 | import math
n0 = 8.0
answer = math.pi * n0**2
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 d 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 | what is the maximum number q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ? | 24 | n0 = 27.0
n1 = 8.0
n2 = 9.0
n3 = 12.0
t0 = 2.0 * 3.0
t1 = n2 * n3 * t0
answer = t1 / n0
print(answer) | MathQA_Geometry |
Geometry | geometry | a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . 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 salaries ? | 216 | n0 = 20.0
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 = t3 * 360.0
t5 = t4 / 100.0
answer = 360.0 - t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the diameter of a circle is 4 / π . find the circumference of the circle . | 8 | import math
n0 = 4.0
t0 = n0 / 3.141592653589793
answer = 2 * math.pi * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular garden is three times its width . if the area of the rectangular garden is 507 square meters , then what is the width of the rectangular garden ? | 13 | import math
n0 = 507.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
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 | the volume of a cube is 343 cc . find its surface . | 294 | n0 = 343.0
t0 = n0**(1 / 3)
answer = 6 * t0**2 # surface of a cube
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ? | 180 | n0 = 28.0
n1 = 24.0
n2 = 15.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the diameter of a cylindrical tin is 10 cm and height is 5 cm . find the volume of the cylinder ? | 125 | import math
n0 = 10.0
n1 = 5.0
t0 = n0 / 2.0
t1 = math.pi * t0**2 * n1
answer = t1 / 3.141592653589793
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ? | 0.78125 | n0 = 2.0
n1 = 7.0
n2 = 64.0
t0 = n0 * n1
t1 = n2 - t0
answer = t1 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | twenty eight 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 ? | 7 | t0 = 10.0 + 4.0
t1 = t0 * 2.0
t2 = t1 / 2.0
answer = t2 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | 10 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 ? | 2.5 | n0 = 10.0
answer = n0 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | an equilateral triangle and three squares are combined as shown above , forming a shape of area 48 + 4 √ 3 . what is the perimeter of the shape formed by the triangle and squares ? | 36 | n0 = 48.0
n1 = 4.0
n2 = 3.0
t0 = n2**min(2.0, 5)
answer = n1 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a tailor trims 4 feet from opposite edges of a square piece of cloth , and 3 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ? | 18 | import math
n0 = 4.0
n1 = 3.0
n2 = 120.0
t0 = n0 * 2.0
t1 = n1 * 2.0
t2 = t0 + t1
t3 = t1 * t0
t4 = t2**min(2.0, 5)
t5 = n2 - t3
t6 = t5 * 4.0
t7 = t6 + t4
t8 = math.sqrt(max(0, t7))
t9 = t2 + t8
answer = t9 / 2.0
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 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches ? | 100 | n0 = 11.0
n1 = 11.0
n2 = 5.5
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 the length of rectangle is three times of its breadth . if the area of rectangle is 6075 sq . m , then calculate the length ? | 135 | import math
n0 = 6075.0
t0 = n0 / 3.0
t1 = math.sqrt(max(0, t0))
answer = t1 * 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters ) | 1.333333 | n0 = 1.0
n1 = 300.0
n2 = 1.0
n3 = 1.0
n4 = 1000.0
n5 = 1.0
n6 = 1.0
n7 = 0.0
t0 = n1 * 1000.0
t1 = 100.0**min(3.0, 5)
t2 = t1 / t0
answer = t2 - 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,10 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? | 0.4 | n0 = 0.0
n1 = 0.0
n2 = 4.0
n3 = 0.0
n4 = 4.0
n5 = 10.0
n6 = 0.0
t0 = n0 + 10.0
answer = 4.0 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the radius of the incircle of the triangle whose sides measure 5 , 12 and 13 units ? | 2 | n0 = 5.0
n1 = 12.0
n2 = 13.0
t0 = n0 + n1
t1 = n0 * n1
t2 = n2 + t0
answer = t1 / t2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m , what is its area ? | 3,060 | n0 = 23.0
n1 = 226.0
t0 = n0 * 2.0
t1 = n1 - t0
t2 = t1 / 4.0
t3 = n0 + t2
answer = t3 * t2 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | 34 . the side surface of a cylinder can is rolled with a rectangular plate . if the height of a cylinder tank is 8 feet and the perimeter of the circular base is 6 feet , what is the diagonal of the rectangular plate ? | 10 | import math
n0 = 34.0
n1 = 8.0
n2 = 6.0
t0 = n1**min(2.0, 5)
t1 = n2**min(2.0, 5)
t2 = t0 + t1
answer = math.sqrt(max(0, t2))
print(answer) | MathQA_Geometry |
Geometry | geometry | when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ? | 1,296 | n0 = 148.0
t0 = 3.0 * 3.0
t1 = t0 * 4.0
answer = t1 * t1
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 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 edge of a cube is 3 a cm . find its surface ? | 54 | n0 = 3.0
answer = 6 * n0**2 # surface of a cube
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 80 cm , find the sum of the perimeters of all the triangles . | 480 | n0 = 2.0
n1 = 1.0
n2 = 3.0
n3 = 2.0
n4 = 1.0
n5 = 80.0
t0 = n5 + n5 + n5 # perimeter of a triangle
answer = t0 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | rectangular tile each of size 20 cm by 30 cm must be laid horizontally on a rectangular floor of size 100 cm by 150 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 floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is : | 25 | n0 = 20.0
n1 = 30.0
n2 = 100.0
n3 = 150.0
t0 = n2 * n3
t1 = n0 * n1
answer = t0 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | in measuring the sides of a rectangle , one side is taken 6 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements . | 0.7 | n0 = 6.0
n1 = 5.0
t0 = n0 * n1
t1 = n0 - n1
t2 = t0 / 100.0
answer = t1 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz | 1.6 | n0 = 90.0
n1 = 2.0
n2 = 8.0
t0 = n1 * n2
answer = t0 / 10.0
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 | in measuring the sides of a rectangle , one side is taken 6 % in excess , and the other 5 % in deficit . find the error percent in the area calculated from these measurements . | 0.7 | n0 = 6.0
n1 = 5.0
t0 = n0 * n1
t1 = n0 - n1
t2 = t0 / 100.0
answer = t1 - t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a triangle is with base 4 m and height 6 m ? | 12 | n0 = 4.0
n1 = 6.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the perimeter , in meters , of a rectangular garden 24 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ? | 64 | n0 = 24.0
n1 = 16.0
n2 = 12.0
t0 = n1 * n2 # area of rectangle
t1 = t0 / n0
answer = 2 * (n0 + t1) # perimetere of rectangle
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 length and width of this rectangle . | 15 | import math
n0 = 300.0
n1 = 70.0
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 | 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 t 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 | a rectangular grass field is 75 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 ? | 1,350 | n0 = 75.0
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 | a volume of 10976 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 ? | 2,744 | n0 = 10976.0
n1 = 4.0
answer = n0 / n1
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 | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ? | 41 | n0 = 20.0
n1 = 210.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ? | 75 | n0 = 37.0
n1 = 64.0
n2 = 19.0
n3 = 27.0
t0 = 1.0 / 3.0
t1 = n1**min(t0, 5)
t2 = n1 / t1
t3 = t2 - t1
t4 = t3 / t2
answer = t4 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ? | 876 | n0 = 36.5
n1 = 1.0
n2 = 16.0
n3 = 8.0
t0 = 6 * n3**2 # surface of a cube
t1 = t0 / n2
answer = n0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ? | 88 | n0 = 20.0
n1 = 680.0
t0 = n1 / n0
t1 = 2 * (n0 + t0) # perimetere of rectangle
answer = t1 - n0
print(answer) | MathQA_Geometry |
Geometry | geometry | a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ? | 0.049 | import math
n0 = 100.0
n1 = 25.0
n2 = 7.0
n3 = 10.0
t0 = math.pi * n0**2
t1 = math.pi * n2**2 * n3
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | in the rectangular coordinate system , points ( 4 , 0 ) and ( – 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c | 4 | import math
n0 = 4.0
n1 = 0.0
n2 = 4.0
n3 = 0.0
t0 = n0**min(2.0, 5)
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is 4 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ? | 100 | n0 = 4.0
n1 = 5.0
t0 = n0 * n1
answer = n1 * t0 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular garden is to be twice as long as it is wide . if 300 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ? | 100 | n0 = 300.0
t0 = 1.0 + 2.0
t1 = t0 * 2.0
t2 = n0 / t1
answer = t2 * 2.0
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 14 and the height of the prism is 8 , what is the volume of the prism ? | 56 | import math
n0 = 14.0
n1 = 8.0
t0 = math.sqrt(max(0, n0))
t1 = t0 * t0 / 2
answer = n1 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a crate measures 6 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 ? | 6 | n0 = 6.0
n1 = 8.0
n2 = 12.0
t0 = n1 * n2
t1 = n0 * t0
t2 = t1 / n2
answer = t2 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 300 m , its area is ? | 3,000 | n0 = 5.0
n1 = 12.0
n2 = 13.0
n3 = 300.0
t0 = n0 + n1
t1 = n2 + t0
t2 = n3 / t1
answer = n3 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | can n and can в are both right circular cylinders . the radius of can n is twice the radius of can b , while the height of can n is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can n with the same brand of gasoline ? | 16 | n0 = 4.0
t0 = n0 * 2.0
t1 = 2.0**min(2.0, 5)
t2 = t1 / 2.0
answer = t2 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | how many odd numbers between 10 and 1,000 are the squares of integers ? | 14 | n0 = 10.0
n1 = 1000.0
answer = n0 + 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | 1,812 | n0 = 25.0
n1 = 15.0
n2 = 12.0
n3 = 2.0
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 | 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 45 cm , find the sum of the perimeters of all the triangles . | 270 | n0 = 2.0
n1 = 1.0
n2 = 3.0
n3 = 2.0
n4 = 1.0
n5 = 45.0
t0 = n5 + n5 + n5 # perimeter of a triangle
answer = t0 + t0
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 a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the shorter sides ? | 8 | import math
n0 = 104.0
n1 = 42.0
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 circular logo is enlarged to fit the lid of a jar . the new diameter is 60 per cent larger than the original . by what percentage has the area of the logo increased ? | 143.36 | n0 = 60.0
t0 = n0 * 2.0
t1 = t0 / 1000.0
t2 = t1 + 3.0
t3 = t2**min(2.0, 5)
t4 = t3 - 4.0
t5 = t4 / 4.0
answer = t5 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is one fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 784 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 5 units ? | 35 | import math
n0 = 784.0
n1 = 5.0
t0 = math.sqrt(max(0, n0))
t1 = t0 / 4.0
answer = n1 * t1 # area of rectangle
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 8 m , the volume of the box ( in m 3 ) is : | 5,120 | n0 = 48.0
n1 = 36.0
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 | three table runners have a combined area of 220 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 ? | 28 | n0 = 220.0
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 | rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ? | 20 | n0 = 10.0
n1 = 18.0
n2 = 9.0
t0 = n0 * n1 # area of rectangle
answer = t0 / n2
print(answer) | MathQA_Geometry |
Geometry | geometry | a triangle has sides 10 , 17 , and 21 . a square is inscribed in the triangle . one side of the square lies on the longest side of the triangle . the other two vertices of the square touch the two shorter sides of the triangle . what is the length of the side of the square ? | 5.793103 | import math
n0 = 10.0
n1 = 17.0
n2 = 21.0
t0 = (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
t1 = t0 * 2.0
t2 = t1 / n2
t3 = t2 / n2
t4 = t3 + 1.0
answer = t2 / t4
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sum of a number and its square is 210 , what is the number ? | 14 | import math
n0 = 210.0
t0 = math.sqrt(max(0, n0))
answer = math.floor(t0)
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ? | 146 | n0 = 10.0
n1 = 680.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular garden is three times its width . if the area of the rectangular garden is 588 square meters , then what is the width of the rectangular garden ? | 14 | import math
n0 = 588.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 15 apiece , what is the total cost for the number of carpet squares needed to cover the floor ? | 225 | n0 = 6.0
n1 = 10.0
n2 = 2.0
n3 = 2.0
n4 = 15.0
answer = n4 * n4
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ? | 147 | n0 = 56.0
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 | 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 | the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2028 sq m , then what is the breadth of the rectangular plot ? | 26 | import math
n0 = 2028.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular grass field is 70 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 ? | 1,300 | n0 = 70.0
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 | the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 20 , what is the perimeter of the garden in feet ? | 40 | n0 = 2.0
n1 = 20.0
answer = n1 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | if a is the smallest positive integer such that 3150 multiplied by a is the square of an integer , then a must be | 14 | n0 = 3150.0
t0 = 1.0 + 4.0
t1 = t0 * t0
t2 = n0 / t1
t3 = t2 / 2.0
t4 = t3 / 3.0
t5 = t4 / 3.0
answer = t5 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ? | 9 | n0 = 30.0
n1 = 30.0
t0 = n0 + 100.0
t1 = 100.0 - n0
t2 = t0 * t1
t3 = t2 / 100.0
answer = 100.0 - t3
print(answer) | MathQA_Geometry |
Geometry | geometry | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ? | 12 | import math
n0 = 36.0
t0 = math.sqrt(max(0, n0))
t1 = math.sqrt(max(0, 2.0))
t2 = t0 * t1
t3 = t2**min(2.0, 5)
t4 = t3 + t3
answer = math.sqrt(max(0, t4))
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular garden is three times its width . if the area of the rectangular garden is 675 square meters , then what is the width of the rectangular garden ? | 15 | import math
n0 = 675.0
t0 = n0 / 3.0
answer = math.sqrt(max(0, t0))
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of each side of an equilateral triangle having an area of 4 â ˆ š 3 cm 2 is ? | 4 | import math
n0 = 4.0
n1 = 3.0
n2 = 2.0
t0 = 1.0 / n2
t1 = math.sqrt(max(0, n1))
t2 = n0 * t1
t3 = t0 * t0
t4 = t3 * t1
t5 = t2 / t4
answer = math.sqrt(max(0, t5))
print(answer) | MathQA_Geometry |
Geometry | geometry | the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ? | 105 | n0 = 42.0
n1 = 5.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ? | 27 | n0 = 9.0
n1 = 3.0
t0 = n0**min(2.0, 5)
answer = t0 / 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot . what will be the length of the diagonal of the square plot ? | 120 | import math
n0 = 90.0
n1 = 80.0
t0 = n0 * n1 # area of rectangle
t1 = math.sqrt(t0) # square edge given area
answer = math.sqrt(t1**2 + t1**2)
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 | a larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 216 smaller cubes and the surface area of the larger cube , in square inch ? | 1,080 | n0 = 216.0
n1 = 216.0
n2 = 1.0
n3 = 216.0
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 | three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 22 square meters . what is the area that is covered with three layers of rug ? | 19 | n0 = 200.0
n1 = 140.0
n2 = 22.0
t0 = n0 - n1
t1 = t0 - n2
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? | 600 | n0 = 7.0
n1 = 1.0
t0 = 6 * n1**2 # surface of a cube
t1 = 6 * n0**2 # surface of a cube
t2 = t0 * t1
t3 = t2 / t1
answer = t3 * 100.0
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 | the diagonals of a rhombus are 12 cm and 20 cm . find its area ? | 120 | n0 = 12.0
n1 = 20.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of an isosceles trapezoid with sides of length 5 and bases of length 11 and 17 is ? | 56 | n0 = 5.0
n1 = 11.0
n2 = 17.0
answer = 4.0 * (n2 + n1) / 2 # quadrilateral area
print(answer) | MathQA_Geometry |
Geometry | geometry | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ? | 10 | import math
n0 = 25.0
t0 = math.sqrt(max(0, n0))
t1 = math.sqrt(max(0, 2.0))
t2 = t0 * t1
t3 = t2**min(2.0, 5)
t4 = t3 + t3
answer = math.sqrt(max(0, t4))
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm ? | 180 | n0 = 24.0
n1 = 9.0
n2 = 6.0
t0 = n1 + n2
t1 = 1.0 / 2.0
t2 = t0 * t1
answer = n0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a circular well with a diameter of 6 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ? | 678.584013 | import math
n0 = 6.0
n1 = 24.0
t0 = n0 / 2.0
answer = math.pi * t0**2 * n1
print(answer) | MathQA_Geometry |