silo height capacity 10,800 pi ft^3

Question

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top. The diameter of the silo is to be 30 feet, but the height is yet to be determined. find the height h of the silo that will result in a capacity of 10,800 pi ft^3

Answer 1

The silo consists of:

1. A cylindrical base.
2. A hemisphere on top.

π(r^2)h + (2/3)​π(r^3) = 10800π

so:

π(15^2)h + (2/3)​π(15^3) = 10800π

therefore:

225h + 2250 = 10800

so the h = 38 feet