Chapter 12.4, Problem 8WE

To determine

To complete: Copy and complete the table for sphere.

Answer to Problem 8WE

Radius is 6 and area is $144\pi$ .

Explanation of Solution

Given information:

The given volume is $288\pi$ .

Calculation:

The Area of sphere is given by

  $A=4\pi r^2$ and

The Volume is given by

  $V=\frac{4}{3}\pi r^3$ .

Here volume $V=288\pi$ . Therefore,

  $\begin{array}{l}\frac{4}{3}\pi r^3=288\pi \\ r^3=288\pi \times \frac{3}{4\pi }\\ r^3=216\\ r=6\end{array}$

Now, Area

  $\begin{array}{l}A=4\pi {\left(6\right)}^2\\ A=4\pi \times 36\\ A=144\pi \end{array}$

Hence,

Radius is 6 and area is $144\pi$ .