Chapter 12.5, Problem 2ST2

To determine

Tofind:The area of sphere if volume is given.

Answer to Problem 2ST2

The required area of sphere is $16\pi {\text{m}}^2$ .

Explanation of Solution

Given information:The volume of sphere is $\frac{32}{3}\pi {\text{m}}^3$ .

Calculation:

The formula for the volume of sphere is $\frac{4}{3}\pi r^3$ and the given volume of sphere is equal to $\frac{32}{3}\pi {\text{m}}^3$ .

Equate both the volumes and solve.

  $\begin{array}{c}\frac{4}{3}\pi r^3=\frac{32}{3}\pi {\text{m}}^3\\ r^3=\frac{32}{3}\pi \times \frac{3}{4\pi }{\text{m}}^3\\ r^3=8{\text{m}}^3\\ r=2\text{m}\end{array}$

So, the radius of the sphere is equal to $2\text{m}$ .

The formula for the area of sphere is $4\pi r^2$ .

Substitute $2$ for $r$ in the formula for area.

  $\begin{array}{c}\text{Area}=4\pi r^2\\ =4\pi {\left(2\text{m}\right)}^2\\ =4\pi \times 4{\text{m}}^2\\ =16\pi {\text{m}}^2\end{array}$

Therefore, the area of sphere is $16\pi {\text{m}}^2$ .