Chapter 12, Problem 15CT

To determine

To find: The volume of a sphere.

Answer to Problem 15CT

The volume of the sphere is $\frac{9\text{π}}{2}$ .

Explanation of Solution

Given information: Area of a sphere is $\text{9π}$ .

Calculation:

To find the volume, first find the radius of the sphere.

The formula for the area of sphere is:

  $A=4\text{π}{r}^2$

Substitute $9\text{π}$ for $A$ in the formula.

  $\begin{array}{c}9\text{π}=4\text{π}{r}^2\\ \frac{9\text{π}}{4\text{π}}=r^2\\ \sqrt{\frac{9}{4}}=r\\ \frac{3}{2}=r\end{array}$

So, the radius of the sphere is $\frac{3}{2}$ .

The formula for the volume of a sphere is:

  $V=\frac{4}{3}\text{π}{r}^3$

Substitute $\frac{3}{2}$ for $r$ in the formula.

  $\begin{array}{c}V=\frac{4}{3}\text{π}\cdot {\left(\frac{3}{2}\right)}^3\\ =\frac{4}{3}\text{π}\cdot \frac{27}{8}\\ =\frac{9\text{π}}{2}\end{array}$

Therefore, the volume of the sphere is $\frac{9\text{π}}{2}$ .