Chapter 12, Problem 28SGR

To determine

To find the volume of given hemisphere.

Answer to Problem 28SGR

3,617 cubic meters

Explanation of Solution

Given:

Circumference of great circle $=24\pi$ meter

Formula used:

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

Volume of a hemisphere $=\frac{2}{3}\pi r^3$ , where $r$ is the radius of the hemisphere.

Calculation:

Circumference of the great circle $=24\pi$

So,

  $\Rightarrow 2\pi r=24\pi$

  $\Rightarrow r=\frac{24\pi }{2\pi }$

  $\Rightarrow r=12$ meters

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

  $V=\frac{2}{3}\pi r^3$

Putting the value of $r$ ,

  $\Rightarrow \frac{2}{3}\times 3.14\times {(12)}^3$

  $\Rightarrow \frac{10851}{3}$

  $\Rightarrow V=3,617$ cubic meters.

Conclusion:

Hence, the volume of the given hemisphere is 3,617 cubic meters.