Chapter 1.3, Problem 51PPS

a)

To determine

To write: an algebraic equation for the formula of volume of a cylinder.

Answer to Problem 51PPS

An algebraic equation for the formula of volume of a cylinder is $V=\pi r^{2}h$.

Explanation of Solution

Given information:

A cylinder is given as shown:

  

Calculation:

Now, radius of base of the cylinder is $r$.

Height is $h$.

Volume is $\pi$ times the radius times the radius times the height.

Formula for volume will be

  $V=\pi r^{2}h$

a)

To determine

To solve: the algebraic expression from part (a) for h.

Answer to Problem 51PPS

  $h=\frac{V}{\pi r^2}$

Explanation of Solution

Given information:

A cylinder is given as shown:

  

Calculation:

Now, radius of base of the cylinder is $r$.

Height is $h$.

Volume is $\pi$ times the radius times the radius times the height.

Formula for volume will be

  $V=\pi r^{2}h$

Now, solve the equation for $h$ as shown:

  $\begin{array}{l}V=\pi r^{2}h\\ \pi r^{2}h=V\\ \frac{\pi r^{2}h}{\pi r^2}=\frac{V}{\pi r^2}\\ h=\frac{V}{\pi r^2}\end{array}$