Chapter 14, Problem 18CPE

To determine

Tofind: the volume of sphere.

Answer to Problem 18CPE

The volume of sphere is $288\pi {\text{cm}}^3$ .

Explanation of Solution

Given information:

The surface area of sphere is $144\pi {\text{cm}}^2$ .

Calculation: to find the volume of the sphere, first find the radius of the sphere,

Since, the area of sphere is $144\pi {\text{cm}}^2$ ,

$\begin{array}{l}4\pi r^2=144\pi {\text{cm}}^2\\ r^2=36\text{ [divide]}\\ r=6\text{cm [sqaure root]}\end{array}$

Now, to find the volume of sphere, use the formula and then substitute and simplify,

$\begin{array}{l}v=\frac{4}{3}\pi r^3\\ v=\frac{4}{3}\pi {\left(6\right)}^3\text{ [susbtitute]}\\ v=288\pi {\text{cm}}^3\text{ [simplify]}\end{array}$

Thus, the volume of sphere is $288\pi {\text{cm}}^3$ .