Chapter 12.4, Problem 12WE

To determine

To find: The diameter of the sphere.

Answer to Problem 12WE

Area of the sphere is $36\pi {\text{ m}}^2$

Explanation of Solution

Given information:

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

Calculation:

The volume of sphere is given by

  $V=\frac{4}{3}\pi r^3$ and

The area of sphere is given by

  $A=4\pi r^2$

Here, volume $V=36\pi {\text{ m}}^3$ . Therefore,

  $\begin{array}{l}\frac{4}{3}\pi r^3=36\pi {\text{ m}}^3\\ r^3=36\pi \times \frac{3}{4\pi }{\text{ m}}^3\\ r^3=27{\text{ m}}^3\\ r=3\text{ m}\end{array}$

Thus, area of the sphere will be

  $\begin{array}{l}A=4\pi r^2\\ A=4\pi {\left(3\right)}^2\\ A=4\pi \times 9\\ A=36\pi {\text{ m}}^2\end{array}$

Hence,

Area of the sphere is $36\pi {\text{ m}}^2$