Chapter 12.8, Problem 17PPS

To determine

To find: Volume of a soccer pavilion that’s diameter is given 66 feet.

Answer to Problem 17PPS

Volume of pavilion is 1653.6 cubic feet.

Explanation of Solution

Given information: Diameter of the regular soccer ball is 8.7 inches and its volume is given as 344.8 cubic inches. Also, the diameter of the pavilion is 66 feet.

Concept/Formula used: Firstly calculate the height of the pavilion using the volume and diameter of the ball. Then use this height to find the volume of the pavilion using below formula:

(i) Volume of the cylinder $=\pi {(\text{radius})}^2\times \text{height}$

(ii) $1\text{feet}=12\text{inches}$

Calculation: Plug in all related values in above formula and calculate for height of ball:

  $\begin{array}{l}\text{344}\text{.8}=3.14\times \frac{8.7}{2}\times \frac{8.7}{2}\times h\\ =\frac{237.78}{4}h=59.44\\ h=\frac{344.8}{59.44}=5.8\text{inches }\\ =\frac{5.8}{12}\text{ feet}=0.4833\text{feet}\end{array}$

So, as height of the pavilion is 5.8 inches and its radius is 33 feet. So, volume of pavilion:

  $\begin{array}{l}\text{Volume of pavilion}=3.14\times 33\times 33\times 0.4833\\ =1653.6\end{array}$

Conclusion: So, volume of the pavilion is calculated as 1653.6 cubic feet.