Chapter 12.4, Problem 5WE

To determine

To complete: Copy and complete the table for sphere.

Answer to Problem 5WE

Radius is 4 and volume is $\frac{256}{3}\pi$ .

Explanation of Solution

Given information:

The given area is $64\pi$ .

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 area $A=64\pi$ . Therefore,

  $\begin{array}{l}4\pi r^2=64\pi \\ r^2=\frac{64\pi }{4\pi }\\ r^2=16\\ r=4\end{array}$ and

Volume

  $\begin{array}{l}V=\frac{4}{3}\pi {\left(4\right)}^3\\ V=\frac{4}{3}\pi \times 64\\ V=\frac{256}{3}\pi \end{array}$

Hence,

Radius is 4 and volume is $\frac{256}{3}\pi$ .