Chapter 12.3, Problem 21PPS

To determine

To calculate: quantity of gallons of water wills the rain barrel will hold.

Answer to Problem 21PPS

Total volume $\left(V\right)$ of the rain barrel which it can hold is $23398.5i{n}^3$ .

Explanation of Solution

Given:

Height of the cylindrical rain barrel $=38inch$

Diameter of the cylindrical rain barrel $=28inch$

Concept used:

The formula for the volume of rain barrel be calculated as,

  $V=\frac{\pi h}{12} \left(2D^2 +d^2\right)$

Where,

  $V=$ volume.

  $D=$ diameter of the top side.

  $d=$ diameter of bottom side.

Calculation:

The formula for the volume of rain barrel be calculated as,

  $V=\frac{\pi h}{12} \left(2D^2 +d^2\right)$

After putting the values in the equation,

  $\begin{array}{l}V=\frac{\pi h}{12} \left(2D^2 +d^2\right)\\ V=\frac{\pi h}{12} \left(\left(2\times {28}^2\right)+\left({28}^2\right)\right)\\ V=\frac{\pi h}{12} \left(2352\right)\\ V=9.94\left(2352\right)\\ V=23398.5i{n}^3\end{array}$

Thus, Total volume $\left(V\right)$ of the rain barrel which it can hold is $23398.5i{n}^3$ .