Chapter 5.1, Problem 71AYU

To determine

To Express: The volume $V$ as a function of $r$ , if height is twice of radius.

Answer to Problem 71AYU

The volume of the cylinder is $V=2\pi r^3$ .

Explanation of Solution

Given information: The volume $V$ of a right circular cylinder of height $\left(h\right)$ and radius $\left(r\right)$ is $V=\pi r^{2}h$ .

Calculation:

The volume of the cylinder, $V=\pi r^{2}h$ .

Here, the height is twice of radius.

Therefore, $h=2r$

Let’s find the volume of the cylinder,

  $\begin{array}{l}V=\pi r^2\left(2r\right)\\ =2\pi r^3\end{array}$

Hence, the volume of the cylinder is $V=2\pi r^3$ .