Chapter 12.6, Problem 24PPS

To determine

To find the volume of given hemisphere to the nearest tenth.

Answer to Problem 24PPS

50 ft³

Explanation of Solution

Given: The circumference of the great circle is given as $18$ ft.

Formula used:

Volume of a hemisphere $=\frac{2}{3}\pi r^3$

And circumference of great circle of a hemisphere $=2\pi r$ , where r is the radius of the hemisphere.

Calculation:

  $\begin{array}{l}2\pi r=18\\ \Rightarrow r=\frac{18}{2\pi }\\ \Rightarrow r=2.865\end{array}$

Volume of given hemisphere,

  $\begin{array}{l}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}·\pi ·{\left(2.865\right)}^3\\ =\frac{2}{3}\times \pi \times 23.51\\ =49.242\\ \sim 50\left(\text{to nearest tenth}\right)\end{array}$

Hence, volume of given hemisphere is 50 ft³.