Chapter 12.6, Problem 22PPS

To determine

To find the volume of given sphere to the nearest tenth.

Answer to Problem 22PPS

1440 m³

Explanation of Solution

Given: The area of the great circle is given as $49\pi$ m².

Formula used:

Volume of a sphere $=\frac{4}{3}\pi r^3$

And area of great circle of a sphere $=\pi r^2$ , where r is the radius of the sphere.

Calculation:

  $\begin{array}{l}\pi r^2=49\pi \\ \Rightarrow r^2=\frac{49\pi }{\pi }\\ \Rightarrow r^2=49\\ \Rightarrow r=7\end{array}$

Volume of given sphere,

  $\begin{array}{l}=\frac{4}{3}\pi r^3\\ =\frac{4}{3}·\pi •{\left(7\right)}^3\\ =\frac{4}{3}\times \pi \times 343\\ =1436.75\\ \sim 1440\left(\text{to nearest tenth}\right)\end{array}$

Hence, volume of given sphere is 1440 m³.