Chapter 12, Problem 29SGR

To determine

To find the volume of given sphere.

Answer to Problem 29SGR

1,696 cubic inches

Explanation of Solution

Given:

Area of great circle $=55\pi$ square inches

Formula used:

Area of a circle $=\pi r^2$ , where $r$ is the radius of the circle.

Volume of a sphere $=\frac{4}{3}\pi r^3$ , where $r$ is the radius of the hemisphere.

Calculation:

Area of the great circle $=55\pi$

So,

  $\Rightarrow \pi r^2=55\pi$

  $\Rightarrow r^2=\frac{55\pi }{\pi }$

  $\Rightarrow r^2=55$

Taking square root on both sides,

  $\Rightarrow r\approx 7.4$ inches

Now for the volume of the given sphere, use the below formula.

  $V=\frac{4}{3}\pi r^3$

Putting the value of $r$ ,

  $\Rightarrow \frac{4}{3}\times 3.14\times {(7.4)}^3$

  $\Rightarrow \frac{5089}{3}$

  $\Rightarrow V=1,696$ cubic inches

Conclusion:

Hence, the volume of the given hemisphere is 1,696 cubic inches.