Chapter 12.6, Problem 23PPS

To determine

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

Answer to Problem 23PPS

180 in³

Explanation of Solution

Given: The circumference of the great circle is given as $22$ in.

Formula used:

Volume of a sphere $=\frac{4}{3}\pi r^3$

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

Calculation:

  $\begin{array}{l}2\pi r=22\\ \Rightarrow r=\frac{22}{2\pi }\\ \Rightarrow r=3.5\end{array}$

Volume of given sphere,

  $\begin{array}{l}=\frac{4}{3}\pi r^3\\ =\frac{4}{3}·\pi ·{\left(3.5\right)}^3\\ =\frac{4}{3}\times \pi \times 42.9\\ =179.6\\ \sim 180\left(\text{to nearest tenth}\right)\end{array}$

Hence, volume of given sphere is 180 in³.