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

Answer:

$V(r) =101\pi r^2 + \frac{2}{3}\pi r^3$

Step-by-step 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

$V_2 = \frac{2}{3}\pi r^3$ ---- hemisphere

So, the volume of the silo is:

$V =V_1 + V_2$

$V =101\pi r^2 + \frac{2}{3}\pi r^3$

Write as a function

$V(r) =101\pi r^2 + \frac{2}{3}\pi r^3$

Where: $\pi = \frac{22}{7}$