Chapter 12.6, Problem 3BCYP

To determine

Find the volume .

Answer to Problem 3BCYP

  $1476.5m{m}^3$

Explanation of Solution

Given:

Hemisphere : area of great circle is about 249 square milimeters

Formula Used:

Volume of a hemisphere:

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

Calculation:

Let the radius of the hemisphere be r

Given , area of the great circle = 249 square mm.

  $\begin{array}{l}A=\pi r^2=249\\ \Rightarrow r^2=\frac{249}{\pi }\mathrm{............}[divide\text{ each side by }\pi \text{]}\\ \Rightarrow r=\sqrt{\frac{249}{\pi }}\mathrm{.........}[take\text{ square root each side]}\\ \Rightarrow r\approx 8.9mm\end{array}$

Radius of the hemisphere = 8.9 mm

Volume of the hemisphere = $V=\frac{2}{3}\pi r^3=\frac{2}{3}\pi {(8.9)}^3\approx 1476.5m{m}^3$

Hence ,

The volume of the hemisphere is $1476.5m{m}^3$