Chapter 12.6, Problem 21PPS

To determine

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

Answer to Problem 21PPS

2710 cm³

Explanation of Solution

Given: The diameter of the hemisphere is 21.8 cm.

Formula used:

Volume of a hemisphere $=\frac{2}{3}\pi r^3$

And radius of a hemisphere (r) $=\frac{d}{2}$ , where r and d are radius and diameter of the hemisphere respectively.

Calculation:

  $\begin{array}{l}r=\frac{21.8}{2}\\ \Rightarrow r=10.9\end{array}$

Volume of given hemisphere,

  $\begin{array}{l}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}·\pi ·{\left(10.9\right)}^3\\ =\frac{2}{3}\times \pi \times 1295.03\\ =2712.3\\ \sim 2710\left(\text{to nearest tenth}\right)\end{array}$

Hence, volume of given hemisphere is 2710 cm³.