Chapter 1.7, Problem 51WE

To determine

To calculate:

Given formula of cylinder for the variable printed.

Answer to Problem 51WE

Variable $\left(h\right)$ for the given formula of cylinder is $\frac{A}{2\pi r}-r$ .

Explanation of Solution

Given information:

  $\begin{array}{l}A=2\pi \left(r+h\right)\\ A=80\pi \\ r=5\end{array}$

Calculations:

Total area of cylinder is given as,

  $A=2\pi \left(r+h\right)$

By using distributive property for opening the parentheses.

  $\begin{array}{l}A=2\pi r\left(r\right)+2\pi r\left(h\right)\\ A=2\pi r^2+2\pi h\end{array}$

Now solve for the variables $h$ ,

First subtract $2\pi r^2$ from both the sides,

  $\begin{array}{l}A-2\pi r^2=2\pi r^2+2\pi rh-2\pi r^2\\ A-2\pi r^2=2\pi rh\end{array}$

Now divide both sides by $2\pi r$

  $\begin{array}{l}\frac{A-2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r}\\ \frac{A}{2\pi r}-r=h\end{array}$

Use the symmetry property,

  $h=\frac{A}{2\pi r}-r$