Question

The volume of a solid hemisphere is $1152\mathrm{\pi }$${\text{cm}}^3$. Find its curved surface area ?

Answer 1

Step 1: Find the radius of the hemisphere

We know that volume of the hemisphere $=\frac{2}{3}{\mathrm{\pi r}}^3$

And Curved surface area $=2{\mathrm{\pi r}}^2$

Here given volume $=1152\mathrm{\pi }$

So,

$$\begin{gathered} \Rightarrow 1152\mathrm{\pi }=\frac{2}{3}{\mathrm{\pi r}}^3 \\ \Rightarrow 1152\cancel{\mathrm{\pi }}=\frac{2}{3}\cancel{\mathrm{\pi }}{\mathrm{r}}^3 \\ \Rightarrow {\mathrm{r}}^3=1152\times \frac{3}{2}=\sout{1152}\times \frac{3}{\sout{2}}=576\times 3=1728 \\ \Rightarrow \mathrm{r}=\sqrt[3]{1728}=12\text{cm} \end{gathered}$$

Step 2: Find the curved surface area

Curved surface area

$$\begin{gathered} =2{\mathrm{\pi r}}^2 \\ =2\times \frac{22}{7}\times 144 \\ =\frac{6336}{7} \\ =905.14{\text{cm}}^2 \end{gathered}$$

Hence, the curved surface area is $905.14{\text{cm}}^2$