To calculate volume
For the answer use cubic units.
Find the volume of the square pyramids given below.
Problem 1 :
Solution :
Base is in the shape of square
Base area = area of square
Area of square = (Side)^{2}
= (32)^{2}
Height = 50 ft
Volume of pyramid = (1/3) x (32)^{2 }x 50
= 17066.6 ft^{3}
Problem 2 :
Solution :
Base area = area of square
height = 6 cm
Area of square = 5^{2}
Volume = (1/3) x 5^{2} x 6
= 50 cm^{3}
Problem 3 :
Solution :
Base area = area of square
height = 8 cm
Area of square = 6^{2}
Volume = (1/3) x 6^{2} x 8
= 96 cm^{3}
Problem 4 :
Solution :
Base area = area of square
Let height = h cm
Slant height = 8 cm
Using Pythagorean theorem h^{2} + 6^{2} = 8^{2} h^{2} + 36 = 64 h^{2} = 64 - 36 h^{2} = 28 h = 5.29 |
Area of square = 12^{2}
= 144
Volume = (1/3) x 144 x 5.29
= 253.92 cm^{3}
Problem 4 :
Find the volume of the square pyramid with a height of 15 in and a slant height of 17 in. The square base measures 16 by 16 inches.
Solution :
Base length of square = 16 inches
height = 15 in
slant height = 17 in
Volume of square pyramid = (1/3) x 16^{2} x 15
= 1280 cubic inches
Problem 5 :
Solution :
Base length = 32 in
Slant height = 34 in
height = h
h^{2} + 16^{2} = 34^{2}
h^{2} + 256 = 1156
h^{2} = 1156 - 256
h^{2} = 900
h = 30
Volume = (1/3) x 32^{2} x 30
= 1024 x 10
= 10240 cubic inches
Problem 6 :
Solution :
When we fold this shape, we will get square base pyramid.
Volume of the square pyramid = (1/3) x base area x height
Base area = 18^{2}
= 324 square feet
Considering the equilateral triangle.
h^{2} + 9^{2} = 18^{2}
h^{2} + 81 = 324
h^{2} = 324 - 81
h^{2} = 243
h = 15.58
Volume = (1/3) x 324 x 15.58
= 108 x 15.58
= 1682.64 cubic ft
Problem 7 :
Solution :
Area of the base = 6^{2} ==> 36
height = 9 in
Volume = (1/3) x 36 x 9
= 108 cubic inches
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM