Question

A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 101 feet and the radius of the hemisphere is r feet. Express the volume of the silo as a function of r.

Answer 1

`V(r) =101\pi r^2 + (2)/(3)\pi r^3`

Explanation:

Given

Shapes: cylinder and hemisphere

`h = 101` --- height of cylinder

Required

The volume of the silo

The volume is calculated as:

Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)

So, we have:

`V_1 = \pi r^2h`

`V_1 = \pi r^2 * 101`

`V_1 = 101\pi r^2` --- cylinder

`V_2 = (2)/(3)\pi r^3` ---- hemisphere

So, the volume of the silo is:

`V =V_1 + V_2`

`V =101\pi r^2 + (2)/(3)\pi r^3`

Write as a function

`V(r) =101\pi r^2 + (2)/(3)\pi r^3`

Where:
`\pi = (22)/(7)`