Chapter 12.6, Problem 6CYU

To determine

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

Answer to Problem 6CYU

1070 cm³

Explanation of Solution

Given: The length of diameter of given hemisphere is 16 cm.

Formula used:

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

And diameter of a hemisphere (d) $=2r$ , where r is the radius of the hemisphere.

Calculation:

  $\begin{array}{l}16=2r\\ \Rightarrow r=\frac{16}{2}\\ \Rightarrow r=8\end{array}$

Volume of given hemisphere,

  $\begin{array}{l}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}·\pi ·{\left(8\right)}^3\\ =\frac{2}{3}\times \pi \times 512\\ =1072.3\\ \sim 1070\left(\text{to nearest tenth}\right)\end{array}$

Hence, volume of given hemisphere is 1070 cm³.