Question

The curved surface area of a hemisphere is 905$\frac{1}{7}$ cm², what is its volume?

Answer 1

Given:
Curved surface area of the hemisphere = $905\frac{1}{7}$ cm²
We know:
Curved surface area of a hemisphere = 2$\mathrm{\pi }$r²

$$\begin{gathered} \Rightarrow 905\frac{1}{7}=2\times \frac{22}{7}\times r^2 \\ \Rightarrow \frac{6336}{7}=2\times \frac{22}{7}\times r^2 \\ \Rightarrow r^2=\frac{6336\times 7}{2\times 22\times 7} \\ \Rightarrow r^2=144 \\ \Rightarrow r=\sqrt{144} \\ \Rightarrow r=12\mathrm{cm} \end{gathered}$$

Now,
Volume of the hemisphere = $\frac{2}{3}\mathrm{\pi }{r}^{\mathit{3}}$
= $\frac{2}{3}\times \frac{22}{7}\times {12}^3$
= 3620.57 cm³