Chapter 12.2, Problem 46STP

To determine

To calculate : To find the surface area of the cylinder in terms of p.

Answer to Problem 46STP

The required surface area of the cylinder is $448\pi {\text{in}}^2$ .

Explanation of Solution

Given information: The cylinder has circumference of 16p and height is 20 in.

Formula used:

The surface area of rectangular prism is,

  $S=2\pi rh+2B$

Calculation :

Let first find the radius of the cylinder:

  $\begin{array}{l}C=2\pi r\\ 16\pi =2\pi r\\ r=8\end{array}$

Now, the surface area of the cylinder is,

  $\begin{array}{l}S=2\pi \left(8\right)\left(20\right)+2\pi {\left(8\right)}^2\\ =320\pi +128\pi \\ =448\pi \end{array}$