Chapter 1.7, Problem 52WE

To determine

To calculate:

Given formula of cone for the variable printed.

Answer to Problem 52WE

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

Explanation of Solution

Given information:

  $\begin{array}{l}A=\pi r\left(s+r\right)\\ A=100\pi \\ r=5\end{array}$

Calculations:

Total area of cone is given as,

  $A=\pi r\left(s+r\right)$

By using distributive property for opening the parentheses.

  $\frac{A}{\pi r}=\frac{\pi r\left(s+r\right)}{\pi r}$

Divide each side by $\pi r$ ,

  $\begin{array}{l}\frac{A}{\pi r}=s+r\\ \frac{A}{\pi r}-r=s+r-r\end{array}$

Subtract $r$ to each side,

  $\frac{A}{\pi r}-r=s$

Therefore, $s=\frac{A}{\pi r}-r$