Chapter 12.4, Problem 33PPS

To determine

To find:

The volume of the cylinder.

Answer to Problem 33PPS

The volume of the cylinder is $\text{678}{\text{.6 in}}^3$ .

Explanation of Solution

Given information:

A cylinder has a surface area of $144\pi$ square inches and a height of $6$ inches.

Calculation:

Apply the surface area formula to solve for $r$ .

  $\begin{array}{c}S=2\pi rh+2B\\ S=2\pi rh+2\pi r^2\\ 144\pi =2\pi r\left(6\right)+2\pi r^2\\ 144\pi =12\pi r+2\pi r^2\\ 72=6r+r^2\\ r^2+6r-72=0\\ \left(r+12\right)\left(r-6\right)=0\end{array}$

Either $\left(r+12\right)=0$ or $\left(r-6\right)=0$ .

  $r=-12$ is not possible so, $r=6$ is the radius.

Volume of the cylinder is:

  $\begin{array}{c}V=BH\\ =\pi r^{2}h\\ =\pi {\left(6\right)}^2\left(6\right)\\ =216\pi \\ \approx 678.6{\text{ in}}^3\end{array}$

Hence the volume of the cylinder is $\text{678}{\text{.6 in}}^3$ .