Answer:
The radius of the Hemisphere is 15.8 cm.
[tex]r=15.8\operatorname{cm}[/tex]Explanation:
The formula for the volume of an hemisphere can be written as;
[tex]V=\frac{2}{3}\pi r^3[/tex]Given that the volume of the hemisphere is;
[tex]8231\operatorname{cm}^3[/tex]We can get the radius of the hemisphere using the formula above.
Firstly let us make r the subject of formula;
[tex]\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \text{multiply through by 3/2} \\ \frac{3}{2}V=\pi r^3 \\ \text{divide through by pi} \\ \frac{3}{2}\frac{V}{\pi}=r^3 \\ \text{cube root both sides} \\ \sqrt[3]{\frac{3}{2}\frac{V}{\pi}}=r \\ r=\sqrt[3]{\frac{3}{2}\frac{V}{\pi}} \end{gathered}[/tex]Lastly let us substitute the given volume V into the derived formula for radius r.
[tex]\begin{gathered} r=\sqrt[3]{\frac{3}{2}\frac{V}{\pi}} \\ r=\sqrt[3]{\frac{3\times8231}{2\times\pi}}=\sqrt[3]{\frac{24693}{2\times\pi}} \\ r=15.78\operatorname{cm} \\ r=15.8\operatorname{cm}\ldots\ldots.(to\text{ the nearest tenth of a centimeter)} \end{gathered}[/tex]Therefore, the radius of the Hemisphere is 15.8 cm.
[tex]r=15.8\operatorname{cm}[/tex]