Chapter 12.4, Problem 22PPS

To determine

To find:

The diameter of the cylinder.

Answer to Problem 22PPS

The diameter of the cylinders should be about $2.52\text{ ft}$ .

Explanation of Solution

Given information:

In a sandcastle competition, contestants are allowed to use only water, shovels, and $10$ cubic feet of sand. To transport the correct amount of sand, they want to create cylinders that are $2$ feet tall to hold enough sand for one contestant.

Calculation:

Given volume is $V=10{\text{ ft}}^3$ and $h=2\text{ ft}$ .

Substitute these values in the volume of the cylinder to find the radius $r$ of the cylinder.

  $\begin{array}{c}V=\pi r^{2}h\\ 10=\pi r^2\left(2\right)\\ \pi r^2=\frac{10}{2}\\ \pi r^2=5\\ r^2=\frac{5}{\pi }\\ r^2\approx 1.59\\ r\approx 1.26\end{array}$

Hence, the diameter of the cylinders should be about $2.52\text{ ft}$ .