Chapter 6.4, Problem 3BGP

To determine

To Find:

The volume of the sphere having surface area about 214.5 square inches.

Answer to Problem 3BGP

  $\text{The volume of a sphere having surface area 214}\text{.5 square inches is about }295.40{\text{ in}}^3$

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 S = 214.5 and solve for V .
• $\begin{array}{l}S=\sqrt[3]{36\pi V^2}\\ S^3=36\pi V^2\mathrm{..........}[\text{take cube both the sides]}\\ {\text{V}}^2=\frac{S^3}{36\pi }\mathrm{.............}[\text{divide each side by }36\pi ]\\ \text{V}=\sqrt{\frac{S^3}{36\pi }}\mathrm{............}[\text{take square root each side]}\\ \text{Substitute S = 214}\text{.5 and solve for V:}\\ \text{V}=\sqrt{\frac{{(214.5)}^3}{36\pi }}\approx 295.40\\ \text{So, the volume of a sphere having surface area 214}\text{.5 square inches is about }295.40{\text{ in}}^3\end{array}$