Question

A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on the top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 4 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 35,500pie cubic feet of grain?

Answer 1

`r=16\ ft`

Explanation:

we know that

The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere

so

`V=\pi r^(2)h+(4)/(6)\pi r^(3)`

In this problem we have

`V=35,500\pi\ ft^(3)`

`h=4D=8r` ----> 4 times the diameter is equal to 8 times the radius

substitute in the formula and solve for r

`35,500\pi=\pi r^(2)(8r)+(4)/(6)\pi r^(3)`

Simplify pi

`35,500=8r^(3)+(4)/(6)r^(3)`

`35,500=r^(3)[8+(4)/(6)]`

`35,500=r^(3)[(52)/(6)]`

`r^(3)=35,500/[(52)/(6)]`

`r=16\ ft`