Chapter 8.4, Problem 61STP

To determine

The height of the shipping cylinder.

Answer to Problem 61STP

  $5ft.$

Explanation of Solution

Given information:

The height of a shipping cylinder is $4$ feet more than the radius. If the volume of the cylinder is $5\pi$ cubic feet, how tall is it? Use the formula $V=\pi \cdot r^2\cdot h$ .

Calculation:

From the given information,height of a shipping cylinder is $4$ feet more than the radius and the volume of the cylinder is $5\pi$ cubic feet.

Plug $5\pi$ for $V$ and $r+4$ for $h$ in the formula $V=\pi \cdot r^2\cdot h$ :

  $\begin{array}{l}5\pi =\pi r^2(r+4)\\ r^3+4r^2-5=0\end{array}$

The equation has one real root $r=1$ .

Thus, the height of the shipping cylinder is $1+4=5ft.$