Chapter 12, Problem 24SGR

To determine

To calculate:To find the volume of the shed

Answer to Problem 24SGR

The volume of conical shed is $564.67fee{t}^3$

Explanation of Solution

Given information:Mr. O built a conical storage shed with a base $14$ feet in diameter and a height of $11$ feet.

Formula Used:

Volume of cone is given by the below formula:

  $Volume=\frac{1}{3}\pi r^{2}h$

Where,

  $r=$ Radius of cone

  $h=$ Height of cone

Calculation:

Given a conical storage shed with a base $14$ feet in diameter and a height of $11$ feet.

Here, dimensions of cone as follows:

  $\begin{array}{l}Radius=\frac{Diameter}{2}=\frac{14}{2}=7feet\\ Height=11feet\end{array}$

Volume of cone is calculated as follows:

  $Volume=\frac{1}{3}\pi r^{2}h$

Substituting the values, volume is

  $\begin{array}{l}Volume=\frac{1}{3}\times \frac{22}{7}\times {\left(7\right)}^2\times 11\\ Volume=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 11\\ Volume=\frac{1}{3}\times \frac{22}{1}\times 7\times 1\times 11\\ Volume=\frac{22\times 77}{3}\\ Volume=564.67\end{array}$

Conclusion:

Hence, volume of conical shed is $564.67fee{t}^3$