Chapter 13.1, Problem 13P

To determine

To find:The percent of the capacity utilized of the cylinder.

Answer to Problem 13P

The percent of the capacity utilized of the cylinderis $93.75\%$ .

Explanation of Solution

Given information:The diameter of the cylinder is $4\text{ft}$ .

Calculation:

The volume of the cylinder is,

  $\begin{array}{c}V=\frac{\pi }{4}{d}^{2}h\\ =\frac{\pi }{4}{\left(4\right)}^{2}h\end{array}$

The volume of the water is,

  $\begin{array}{c}{V}_w=\frac{\pi }{4}{d}^{2}h\\ =\frac{\pi }{4}{\left(1\right)}^{2}h\\ =\frac{\pi }{4}h\end{array}$

The percentage of utilization is,

  $\begin{array}{c}\%=\frac{\frac{\pi }{4}{\left(4\right)}^{2}h-\frac{\pi }{4}h}{\frac{\pi }{4}{\left(4\right)}^{2}h}\times 100\%\\ =\frac{15}{16}\times 100\%\\ =93.75\%\end{array}$

Thus, the percent of the capacity utilized of the cylinder is $93.75\%$ .