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Geometry | geometry | the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.90 per metre . | 6,466.69871 | import math
n0 = 13.86
n1 = 4.9
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 roof of an apartment building is rectangular and its length is 5 times longer than its width . if the area of the roof is 720 feet squared , what is the difference between the length and the width of the roof ? | 48 | import math
n0 = 5.0
n1 = 720.0
t0 = n1 / n0
t1 = math.sqrt(max(0, t0))
t2 = t1 * n0
answer = t2 - t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each . the radius of the sphere is | 3 | import math
n0 = 6.0
t0 = n0 / 2.0
t1 = 4.0 * 3.141592653589793
t2 = n0 * t0
t3 = t2 * 3.141592653589793
t4 = t3 * 2.0
t5 = t4 / t1
answer = math.sqrt(max(0, t5))
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 6 , 0 ) , ( 0 , - 3.5 ) , ( - 6 , 0 ) ? | 42 | n0 = 0.0
n1 = 3.5
n2 = 6.0
n3 = 0.0
n4 = 0.0
n5 = 3.5
n6 = 6.0
n7 = 0.0
t0 = n2 * 2.0
t1 = n1 * 2.0
answer = t0 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 30 - sided polygon have ? | 405 | n0 = 30.0
t0 = n0 - 3.0
t1 = n0 * t0
answer = t1 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the width of a rectangular hall is ½ of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ? | 8 | import math
n0 = 128.0
t0 = 1.0 / 2.0
t1 = n0 / t0
t2 = math.sqrt(max(0, t1))
answer = t2 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the 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 . 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | 7,248 | n0 = 25.0
n1 = 15.0
n2 = 12.0
n3 = 8.0
n4 = 6.0
n5 = 3.0
n6 = 4.0
n7 = 3.0
t0 = n0 + n1
t1 = n2 * 2.0
t2 = n4 * 3.0
t3 = n5 * n6
t4 = t0 * t1
t5 = n5 * t3
t6 = t4 - t2
t7 = t6 - t5
answer = n3 * t7
print(answer) | MathQA_Geometry |
Geometry | geometry | rectangular tile each of size 25 cm by 65 cm must be laid horizontally on a rectangular floor of size 150 cm by 390 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 : | 36 | n0 = 25.0
n1 = 65.0
n2 = 150.0
n3 = 390.0
t0 = n2 * n3
t1 = n0 * n1
answer = t0 / t1
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 s 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 | a 25 cm wide path is to be made around a circular garden having a diameter of 4 meters . approximate area of the path is square meters is | 3.337942 | import math
n0 = 25.0
n1 = 4.0
t0 = n1 / 2.0
t1 = n0 / 100.0
t2 = t0 + t1
t3 = math.pi * t0**2
t4 = math.pi * t2**2
answer = t4 - t3
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 $ 220 . 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 $ 270 for the purchase ? | 3 | n0 = 2.0
n1 = 4.0
n2 = 220.0
n3 = 1.0
n4 = 6.0
n5 = 190.0
n6 = 270.0
t0 = n2 / n0
t1 = n5 - t0
t2 = t1 / n1
t3 = n4 * t2
t4 = n5 - t3
t5 = t2 + t4
answer = n6 / t5
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a triangle are 26 cm , 25 cm and 10 cm , what is its area ? | 125 | n0 = 26.0
n1 = 25.0
n2 = 10.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangle has a perimeter of 176 inches . the length of the rectangle is 8 inches more than its width . what is the area of the rectangle ? | 1,920 | n0 = 176.0
n1 = 8.0
t0 = n0 / 2.0
t1 = t0 - n1
t2 = t1 / 2.0
t3 = n1 + t2
answer = t3 * t2 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a certain rectangular crate measures 8 feet by 12 feet by 14 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ? | 6 | import math
n0 = 8.0
n1 = 12.0
n2 = 14.0
t0 = n1 / 2.0
t1 = n0 * 3.141592653589793
t2 = math.pi * t0**2 * n0
t3 = t2 / t1
answer = math.sqrt(max(0, t3))
print(answer) | MathQA_Geometry |
Geometry | geometry | a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter were to make a similar sandbox twice as long , twice as wide , and twice as high as the first sandbox , what would be the capacity , in cubic feet , of the second sandbox ? | 80 | n0 = 10.0
t0 = 2.0**min(3.0, 5)
answer = n0 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a base of a cone is 30 cm 2 . if the height of the cone is 6 cm , find its volume ? | 60 | n0 = 30.0
n1 = 2.0
n2 = 6.0
t0 = n0 * n2
answer = t0 / 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ? | 70 | n0 = 40.0
t0 = 3600.0 / 10.0
t1 = n0 * 2.0
t2 = t0 - t1
answer = t2 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is ? | 48 | n0 = 5.0
n1 = 9.0
n2 = 15.0
answer = 4.0 * (n2 + n1) / 2 # quadrilateral area
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 . 25 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ? | 100 | n0 = 25.0
t0 = 1.0 + 3.0
t1 = t0 + 1.0
t2 = t1**min(3.0, 5)
answer = t2 - n0
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of a square field whose diagonal of length 28 m ? | 392 | n0 = 28.0
t0 = n0**2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the breath of a rectangular landscape is 8 times its length . there is a playground in it whose area is 3200 square mtr & which is 1 / 9 rd of the total landscape . what is the breath of the landscape ? | 480 | import math
n0 = 8.0
n1 = 3200.0
n2 = 1.0
n3 = 9.0
t0 = n1 * n3
t1 = t0 / n0
t2 = math.sqrt(max(0, t1))
answer = n0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a triangle is with base 18 m and height 6 m ? | 54 | n0 = 18.0
n1 = 6.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ? | 4,200 | n0 = 90.0
n1 = 60.0
n2 = 10.0
n3 = 3.0
t0 = n0 + n1
t1 = t0 - n2
t2 = n2 * t1
answer = n3 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | the side of a square is increased by 30 % then how much % does its area increases ? | 69 | n0 = 30.0
t0 = n0 + 100.0
t1 = 100.0**2
t2 = t0**2
t3 = t2 - t1
t4 = t3 * 100.0
answer = t4 / t1
print(answer) | MathQA_Geometry |
Geometry | geometry | one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square | 120 | import math
n0 = 15.0
n1 = 17.0
t0 = n1**min(2.0, 5)
t1 = n0**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
answer = n0 * t3 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ? | 1,323 | n0 = 21.0
t0 = 3.0 + 4.0
t1 = n0 - 1.0
t2 = n0 * t1
t3 = t1 - 1.0
t4 = t2 * t3
t5 = t4 / 3.0
t6 = t5 / 2.0
answer = t6 - t0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm ? | 600 | n0 = 25.0
n1 = 30.0
t0 = 10.0 * 2.0
t1 = t0 * 2.0
answer = n1 * t1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | how many diagonals does a polygon with 15 sides have , if one of its vertices does not connect to any diagonal ? | 77 | n0 = 15.0
t0 = n0 - 1.0
t1 = t0 - 3.0
t2 = t0 * t1
answer = t2 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes . if field has a length that is twice its width , find the area of the field in square meters . | 20,000 | n0 = 10.0
n1 = 12.0
n2 = 30.0
t0 = n1 / 2.0
t1 = t0 / n0
t2 = t1 * 1000.0
t3 = t2 / 2.0
t4 = t3 / 3.0
t5 = t4 * 2.0
answer = t4 * t5 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | if the sides of a triangle are 26 cm , 18 cm and 10 cm , what is its area ? | 90 | n0 = 26.0
n1 = 18.0
n2 = 10.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular garden is to be twice as long as it is wide . if 240 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ? | 80 | n0 = 240.0
t0 = 1.0 + 2.0
t1 = t0 * 2.0
t2 = n0 / t1
answer = t2 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1430 . the perimeter of the plot is ? | 220 | n0 = 10.0
n1 = 6.5
n2 = 1430.0
t0 = n2 / n1
t1 = t0 / 2.0
t2 = t1 - n0
t3 = t2 / 2.0
t4 = t3 + n0
t5 = t4 + t3
answer = t5 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm . | 54 | import math
n0 = 15.0
n1 = 12.0
t0 = n0**min(2.0, 5)
t1 = n1**min(2.0, 5)
t2 = t0 - t1
t3 = math.sqrt(max(0, t2))
t4 = n1 * t3
answer = t4 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | 36 | t0 = 2.0 * 2.0
t1 = t0 * 3.0
answer = t1 * 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a rectangle is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the rectangular field ? | 20 | import math
n0 = 460.0
n1 = 15.0
t0 = n1 / 100.0
t1 = t0 + 1.0
t2 = n0 / t1
answer = math.sqrt(max(0, t2))
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 52 ) square inches . what is the perimeter of the photograph , in inches ? | 10 | n0 = 1.0
n1 = 3.0
n2 = 52.0
t0 = n1 * 2.0
t1 = n0 * 2.0
t2 = t0**min(2.0, 5)
t3 = t1**min(2.0, 5)
t4 = t2 - t3
t5 = n2 - t4
answer = t5 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of a cube is 1728 cc . find its surface ? | 864 | n0 = 1728.0
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 26 cm , 24 cm and 20 cm , what is its area ? | 240 | n0 = 26.0
n1 = 24.0
n2 = 20.0
t0 = n1 * n2
answer = t0 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the diagonals of a rhombus are 14 cm and 18 cm . find its area ? | 126 | n0 = 14.0
n1 = 18.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ? | 22 | n0 = 7.0
n1 = 18.0
t0 = n1 - n0
answer = t0 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cubical block of metal weighs 3 pounds . how much will another cube of the same metal weigh if its sides are twice as long ? | 24 | n0 = 3.0
t0 = 2.0 * 4.0
answer = n0 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level . | 11.25 | n0 = 15.0
n1 = 20.0
n2 = 15.0
t0 = n0 * n1
t1 = n0**3
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is : | 1,200 | n0 = 15.0
n1 = 12.0
t0 = n1 * 2.0
t1 = n0 * 2.0
t2 = n0 * n1 # area of rectangle
t3 = t0 + t1
t4 = t2 * 2.0
t5 = t4 / t3
answer = n0 * n1 * t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ? | 160 | import math
n0 = 1600.0
n1 = 10.0
t0 = n1 / 2.0
t1 = math.sqrt(max(0, n0))
t2 = t1 / t0
t3 = t2 * 2.0
answer = n1 * t3
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ? | 40 | n0 = 200.0
t0 = 1.0 + 1.0
t1 = t0 * 2.0
t2 = t1 + 1.0
t3 = t2 * 2.0
t4 = t3 + t3
t5 = t2 + t3
t6 = t4 + t3
t7 = t5 + t2
t8 = n0 / t7
answer = t6 + t8
print(answer) | MathQA_Geometry |
Geometry | geometry | 50 square stone slabs of equal size were needed to cover a floor area of 98 sq . m . find the length of each stone slab ? | 140 | import math
n0 = 50.0
n1 = 98.0
t0 = n1 / n0
t1 = math.sqrt(max(0, t0))
answer = t1 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ? | 0.111111 | n0 = 20.0
n1 = 812.0
n2 = 140.0
n3 = 60.0
n4 = 84.0
n5 = 100.0
t0 = 4.0 * 4.0
t1 = 2.0 * 4.0
t2 = t0 / 2.0
t3 = n0 - t1
t4 = t3 / 2.0
t5 = t4 * t3
answer = t2 / t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 768 feet squared , what is the difference between the length and the width of the roof ? | 32 | import math
n0 = 3.0
n1 = 768.0
t0 = n1 / n0
t1 = math.sqrt(max(0, t0))
t2 = t1 * n0
answer = t2 - t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 268 meters and 380 meters . find the difference between the areas of the larger and the smaller circles . | 5,775.414575 | import math
n0 = 268.0
n1 = 380.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | what will be the cost of building a fence around a square plot with area equal to 25 sq ft , if the price per foot of building the fence is rs . 58 ? | 1,160 | import math
n0 = 25.0
n1 = 58.0
t0 = math.sqrt(max(0, n0))
t1 = 4 * t0
answer = n1 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the monthly rent of a shop of dimension 18 feet × 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ? | 120 | n0 = 18.0
n1 = 20.0
n2 = 3600.0
t0 = 10.0 + 2.0
t1 = n0 * n1 # area of rectangle
t2 = n2 / t1
answer = t0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ? | 1,520 | n0 = 4.0
n1 = 5.0
n2 = 2.0
n3 = 20.0
t0 = 2 * (n0 * n1 + n0 * n2 + n1 * n2) # surface of a rectangular prism
answer = n3 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a larger cube has 343 cubic inch as a volume and in the cube there are 343 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 343 smaller cubes and the surface area of the larger cube , in square inch ? | 1,764 | n0 = 343.0
n1 = 343.0
n2 = 1.0
n3 = 343.0
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 | what will be the cost of house to paint which area equal to 484 sq ft , if the price per foot of building is rs . 20 | 1,760 | import math
n0 = 484.0
n1 = 20.0
t0 = math.sqrt(max(0, n0))
t1 = t0 * 4.0
answer = n1 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ? | 9,200 | n0 = 15.0
n1 = 20.0
t0 = n0 + 100.0
t1 = 100.0 - n1
answer = t0 * t1
print(answer) | MathQA_Geometry |
Geometry | geometry | find the perimeter and area of a square of side 9 cm . | 81 | n0 = 9.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the perimeter of δ acd is 9 + 3 √ 3 , what is the perimeter of equilateral triangle δ abc ? | 18 | import math
n0 = 9.0
n1 = 3.0
n2 = 3.0
t0 = n1 * 2.0
t1 = math.sqrt(max(0, 3.0))
t2 = 3.0 - t1
t3 = t0 * t2
t4 = t3 / t2
answer = n1 * t4
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular pig farm has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 1250 square feet , what is the total length of the fence , in feet ? | 150 | import math
n0 = 1250.0
t0 = n0 / 2.0
t1 = math.sqrt(max(0, t0))
t2 = t1 * 2.0
answer = 2 * (t2 + t1) # perimetere of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ? | 21 | n0 = 3.78
n1 = 5.25
t0 = n0 * 100.0
t1 = t0 / 3.0
t2 = t1 / 3.0
t3 = t2 / 3.0
t4 = t3 / 2.0
answer = t4 * 3.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles , all of the same size . the minimum number of such tiles is : | 450 | n0 = 3.78
n1 = 5.25
t0 = 3.0 + 4.0
t1 = n0 * 100.0
t2 = n1 * 100.0
t3 = t1 * t2
t4 = t0 * 3.0
t5 = t4**min(2.0, 5)
answer = t3 / t5
print(answer) | MathQA_Geometry |
Geometry | geometry | the surface of a cube is 54 sq cm . find its volume ? | 27 | import math
n0 = 54.0
t0 = 2.0 + 4.0
t1 = n0 / t0
t2 = math.sqrt(max(0, t1))
answer = t2**3
print(answer) | MathQA_Geometry |
Geometry | geometry | if each edge of a cube is doubled , then its volume : | 8 |
answer = 2.0**min(3.0, 5)
print(answer) | MathQA_Geometry |
Geometry | geometry | a lamp is put on one corner of a square plot of side 50 m . it ' s light reaches 21 m . find the area of that plot that is lit by that lamp ? | 346.36059 | import math
n0 = 50.0
n1 = 21.0
t0 = math.pi * n1**2
answer = t0 / 4.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 24 inches and the width of the wall is 42 inches , what is the length of the wall , in inches ? | 27.428571 | n0 = 24.0
n1 = 42.0
t0 = n0**2
t1 = t0 * 2.0
answer = t1 / n1
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ? | 70 | n0 = 30.0
n1 = 600.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the area of square field whose side of length 5 m ? | 25 | n0 = 5.0
answer = n0**2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ? | 59 | n0 = 20.0
n1 = 390.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm . | 120 | import math
n0 = 13.0
n1 = 24.0
t0 = n1 / 2.0
t1 = n0**min(2.0, 5)
t2 = t0**min(2.0, 5)
t3 = t1 - t2
t4 = math.sqrt(max(0, t3))
t5 = t4 * 2.0
answer = n1 * t5 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular floor is covered by a rug except for a strip 2 meters wide along each of the four edge . if the floor is 10 meters by 8 meters , what is the area of the rug in square meters ? | 24 | n0 = 2.0
n1 = 10.0
n2 = 8.0
t0 = n0 * 2.0
t1 = n1 - t0
t2 = n2 - t0
answer = t1 * t2 # area of rectangle
print(answer) | MathQA_Geometry |
Geometry | geometry | find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ? | 90 | n0 = 20.0
n1 = 5.0
n2 = 4.0
t0 = n1 + n2
t1 = 1.0 / 2.0
t2 = t0 * t1
answer = n0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | find the base k of the number system , if ( 524 ) 8 = ( 664 ) k ? | 7 | import math
n0 = 524.0
n1 = 8.0
n2 = 664.0
t0 = 10.0 / 2.0
t1 = n1 * 2.0
t2 = n1**min(2.0, 5)
t3 = t0 * t2
t4 = t1 + t3
t5 = t4 + 4.0
t6 = 4.0 - t5
t7 = t6 / 3.0
t8 = t7 / 2.0
t9 = t8 * 4.0
t10 = 1.0 - t9
t11 = math.sqrt(max(0, t10))
t12 = t11 - 1.0
answer = t12 / 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | a circle graph shows how the budget of a certain company was spent : 61 percent for salaries , 10 percent for research and development , 6 percent for utilities , 5 percent for equipment , 3 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ? | 54 | n0 = 61.0
n1 = 10.0
n2 = 6.0
n3 = 5.0
n4 = 3.0
t0 = n0 + n1
t1 = n2 + t0
t2 = n3 + t1
t3 = n4 + t2
t4 = 100.0 - t3
t5 = t4 * 360.0
answer = t5 / 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | four horses are tethered at four corners of a square plot of side 63 metres so that they just can not reach one another . the area left ungrazed is : | 851.754689 | n0 = 63.0
t0 = n0 / 2.0
t1 = n0 * n0
t2 = 0.25 * 4.0
t3 = t2 * 3.141592653589793
t4 = t0 * t3
t5 = t0 * t4
answer = t1 - t5
print(answer) | MathQA_Geometry |
Geometry | geometry | if a 1 mm thick paper is folded so that the area is halved at every fold , then what would be the thickness of the pile after 50 folds ? | 1 | import math
n0 = 1.0
n1 = 50.0
t0 = n0 * 2.0
answer = math.log(max(1e-5, t0), 2)
print(answer) | MathQA_Geometry |
Geometry | geometry | if each side of a right triangle is increased by 10 % and the base ( b ) is half of the height , find the percentage change in its area ? | 21 | n0 = 10.0
t0 = n0 + 100.0
t1 = t0 / 100.0
t2 = t1**min(2.0, 5)
t3 = t2 - 1.0
answer = t3 * 100.0
print(answer) | MathQA_Geometry |
Geometry | geometry | the circumferences of two circles are 264 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ? | 33,893.636681 | import math
n0 = 264.0
n1 = 704.0
t0 = 2.0 * 3.141592653589793
t1 = n1 / t0
t2 = n0 / t0
t3 = math.pi * t1**2
t4 = math.pi * t2**2
answer = t3 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown . ab = 8 cm and bc = 4 cm . the perimeter of the figure abcpqra ( in cm ) is : | 24 | n0 = 8.0
n1 = 4.0
t0 = n0 + n1
answer = t0 * 2.0
print(answer) | MathQA_Geometry |
Geometry | geometry | susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made | 194 | n0 = 5.0
n1 = 7.0
n2 = 7.0
n3 = 6.0
t0 = n1 * n1
t1 = n1 - 2.0
t2 = n3 - 2.0
t3 = n3 * t0
t4 = t1 * t1
t5 = t4 * t2
answer = t3 - t5
print(answer) | MathQA_Geometry |
Geometry | geometry | in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ? | 32 | n0 = 1.0
n1 = 0.0
n2 = 7.0
n3 = 4.0
n4 = 7.0
n5 = 4.0
t0 = n0 + n2
t1 = n3 * t0 / 2
answer = t1 * 2.0
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 2 liters of water cost ? | 50 | n0 = 1.0
n1 = 1.0
n2 = 50.0
n3 = 1.0
n4 = 2.0
t0 = n0 + n4
t1 = n0 / t0
t2 = n2 * t1
answer = t0 * t2
print(answer) | MathQA_Geometry |
Geometry | geometry | a square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely . if a side of the first square is 4 cm , determine the sum of the areas all the square . | 32 | n0 = 4.0
t0 = 1.0 / 2.0
t1 = n0**min(2.0, 5)
answer = t1 / t0
print(answer) | MathQA_Geometry |
Geometry | geometry | the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ? | 141.371669 | n0 = 15.0
n1 = 3.0
t0 = n1 * 3.141592653589793
answer = n0 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ? | 275 | n0 = 1.0
n1 = 3.0
n2 = 50.0
t0 = n2 * n1
t1 = t0 / 2.0
t2 = n1 * t1
answer = n2 + t2
print(answer) | MathQA_Geometry |
Geometry | geometry | 20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? | 330 | n0 = 20.0
n1 = 7.0
t0 = n0 * n1
t1 = n0 - 1.0
t2 = n0 * t1
t3 = t2 / 2.0
answer = t3 + t0
print(answer) | MathQA_Geometry |
Geometry | geometry | 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 | a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ? | 276 | n0 = 45.0
n1 = 20.0
n2 = 320.0
n3 = 7500.0
t0 = n3 / n1
t1 = n0 / n1
t2 = t0 - n2
t3 = t1 - 1.0
t4 = t2 / t3
answer = n2 - t4
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? | 6 | import math
n0 = 48.0
n1 = 2.0
n2 = 4.0
n3 = 48.0
t0 = n0 * n1
t1 = -n2
t2 = n2**min(n1, 5)
t3 = n2 * t0
t4 = t3 + t2
t5 = math.sqrt(max(0, t4))
t6 = t1 + t5
t7 = t6 / n1
answer = n0 / t7
print(answer) | MathQA_Geometry |
Geometry | geometry | sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour . if the empty rectangular box is 7 feet long , 6 feet wide , and 2 feet deep , approximately how many hours does it take to fill the box ? | 21 | n0 = 4.0
n1 = 7.0
n2 = 6.0
n3 = 2.0
t0 = n1 * n2
t1 = n3 * t0
answer = t1 / n0
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 810 sq . feet , how many feet of fencing will be required ? | 84 | n0 = 30.0
n1 = 810.0
t0 = n1 / n0
t1 = t0 * 2.0
answer = n0 + t1
print(answer) | MathQA_Geometry |
Geometry | geometry | a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path . | 2 | import math
n0 = 15.0
n1 = 10.0
n2 = 54.0
n3 = 2.0
t0 = 2 * (n0 + n1) # perimetere of rectangle
t1 = t0 / 4.0
t2 = t1**min(2.0, 5)
t3 = n2 + t2
t4 = math.sqrt(max(0, t3))
answer = t4 - t1
print(answer) | MathQA_Geometry |
Geometry | geometry | the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone . | 157.079633 | n0 = 10.0
n1 = 5.0
t0 = n1 * 3.141592653589793
answer = n0 * t0
print(answer) | MathQA_Geometry |
Geometry | geometry | a cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm . the radius of the cone will be : | 8 | import math
n0 = 8.0
n1 = 2.0
n2 = 6.0
t0 = math.pi * n0**2 * n1
t1 = t0 * 3.0
t2 = t1 / n2
t3 = t2 / 3.141592653589793
answer = math.sqrt(max(0, t3))
print(answer) | MathQA_Geometry |
Geometry | geometry | the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ? | 32 | n0 = 4.0
n1 = 2.0
n2 = 0.15
n3 = 8.0
n4 = 0.3
answer = n0 * n3
print(answer) | MathQA_Geometry |
Geometry | geometry | the second angle of a triangle is double the first ( 110 ) . the third angle is 40 less than the first ( 15 ) . find the first angle . | 55 | n0 = 110.0
n1 = 40.0
n2 = 15.0
answer = n1 + n2
print(answer) | MathQA_Geometry |
Geometry | geometry | if the length , breadth and the height of a cuboid are in the ratio 6 : 5 : 4 and if the total surface area is 33300 cm 2 cm 2 , then the length , breadth and height in cms , are respectively . | 90 | import math
n0 = 6.0
n1 = 5.0
n2 = 4.0
n3 = 33300.0
n4 = 2.0
n5 = 2.0
t0 = n0 * n1
t1 = n1 * n2
t2 = n0 * n2
t3 = t0 + t1
t4 = t3 + t2
t5 = t4 * 2.0
t6 = n3 / t5
t7 = math.sqrt(max(0, t6))
answer = n0 * t7
print(answer) | MathQA_Geometry |
Geometry | geometry | what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 . | 34.142136 | import math
n0 = 50.0
t0 = n0 * 2.0
t1 = math.sqrt(max(0, 2.0))
t2 = math.sqrt(max(0, t0))
t3 = t2 * t1
answer = t3 + t2 + t2 # perimeter of a triangle
print(answer) | MathQA_Geometry |
Geometry | geometry | the area of a triangle is with base 3 m and height 6 m ? | 9 | n0 = 3.0
n1 = 6.0
answer = n0 * n1 / 2
print(answer) | MathQA_Geometry |
Geometry | geometry | the volume of a cube is 1728 cc . find its surface . | 864 | n0 = 1728.0
t0 = n0**(1 / 3)
answer = 6 * t0**2 # surface of a cube
print(answer) | MathQA_Geometry |
Geometry | geometry | if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ? | 8 | import math
n0 = 120.0
n1 = 46.0
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 length of rectangle is thrice its breadth and its perimeter is 88 m , find the area of the rectangle ? | 363 | n0 = 88.0
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 |