Chapter 6.4, Problem 3AGP

To determine

To Find:

The surface area of the sphere having volume 200 cubic inches.

Answer to Problem 3AGP

The surface area of the sphere having volume 200 cubic inches is about $165.4i{n}^2$ .

Explanation of Solution

Given Information:

The surface area of a sphere can be determined from the volume of the sphere using the formula $S=\sqrt[3]{36\pi V^2}$ , where V is the volume.

Calculation:

• Given$S=\sqrt[3]{36\pi V^2}$
• Substitute V = 200 and solve for S .
• $\begin{array}{l}S=\sqrt[3]{36\pi V^2}\\ =\sqrt[3]{36\pi {(200)}^2}\\ =\sqrt[3]{1440000\pi }\\ =165.388\approx 165.4i{n}^2\end{array}$
• So,the surface area of the sphere having volume 200 cubic inches is about $165.4i{n}^2$ .