Chapter 12.4, Problem 49STP

To determine

To find:

The radius of the cylindrical tank.

Answer to Problem 49STP

The radius of the cylindrical tank is $89.4\text{ ft}$ .

Explanation of Solution

Given information:

A cylindrical tank used for oil storage has a height that is half the length of its radius. Volume of the tank is $1122360{\text{ ft}}^3$ .

Calculation:

A cylindrical tank used for oil storage has a height that is half the length of its radius.

Assume that the radius of the cylindrical tank is $r\text{ ft}$ .

So, the height of the tank is $\frac{r}{2}\text{ ft}$ .

Volume of the cylindrical tank is $V=\pi r^{2}h$ .

Substitute $V=1122360$ and $h=\frac{r}{2}$ in the above to find radius.

  $\begin{array}{c}1122360=\pi r^2\frac{r}{2}\\ 2244720=\pi r^3\\ r^3=\frac{2244720}{\pi }\\ r^3=714516.57\\ r=\sqrt[3]{714516.57}\\ =89.4\text{ ft}\end{array}$

Hence, the radius of the cylindrical tank is $89.4\text{ ft}$ .