Chapter 12.4, Problem 4WE

To determine

To complete: Copy and complete the table for sphere.

Answer to Problem 4WE

Area is $\frac{9}{4}\pi k^2$ and volume is $\frac{9}{16}\pi k^3$ .

Explanation of Solution

Given information:

The given radius is $\frac{3}{4}k$ .

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 $r=\frac{3}{4}k$ . Therefore,

Area

  $\begin{array}{l}A=4\pi {\left(\frac{3}{4}k\right)}^2\\ A=4\pi \times \frac{9}{16}{k}^2\\ A=\frac{9}{4}\pi k^2\end{array}$ and

Volume

  $\begin{array}{l}V=\frac{4}{3}\pi {\left(\frac{3}{4}k\right)}^3\\ V=\frac{4}{3}\pi \times \frac{27}{64}{k}^3\\ V=\frac{9}{16}\pi k^3\end{array}$

Hence,

Area is $\frac{9}{4}\pi k^2$ and volume is $\frac{9}{16}\pi k^3$ .