Question

Volume of a hemisphere is 18000 $\mathrm{\pi }$ cubic cm. Find its diameter.

Answer 1

Let the radius of the hemisphere be r cm.

Volume of the hemisphere = 18000$\mathrm{\pi }$ cm³

$$\begin{gathered} \therefore \frac{2}{3}\mathrm{\pi }{r}^3=18000\mathrm{\pi }{\mathrm{cm}}^3 \\ \Rightarrow r^3=\frac{18000\times 3}{2}=27000 \\ \Rightarrow r^3={\left(30\right)}^3 \\ \Rightarrow r=30\mathrm{cm} \end{gathered}$$
∴ Diameter of the hemisphere = 2r = 2 × 30 = 60 cm

Thus, the diameter of the hemisphere is 60 cm.