Question

4. Find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in. and whose upper base is a square with a side 3 in., and whose altitude is 12 in. Round your answer to the nearest whole number.

Answer 1

the height of the complete pyramid which has a square base of length 5 can be found using similar triangles:-

3/5 = x / (x+12)

x = 0.6x + 7.3
0.4x = 7.2
x = 18
so height of full pyramid is 30 and volume of the frustum is

1/3 * 5^2 * 30 - 1/3 * 3^2 * 18

= 196 in^2