Chapter 12.4, Problem 6WE

To determine

To complete: Copy and complete the table for sphere.

Answer to Problem 6WE

Radius is 9 and volume is $972\pi$ .

Explanation of Solution

Given information:

The given area is $324\pi$ .

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 $A=324\pi$ . Therefore,

  $\begin{array}{l}4\pi r^2=324\pi \\ r^2=\frac{324\pi }{4\pi }\\ r^2=81\\ r=9\end{array}$ and

Volume

  $\begin{array}{l}V=\frac{4}{3}\pi {\left(9\right)}^3\\ V=\frac{4}{3}\pi \times 729\\ V=972\pi \end{array}$

Hence,

Radius is 9 and volume is $972\pi$ .