Question

The volume of a right circular cone of height 24cm² is 1232cm³. Find its curved surface area.

Answer 1

Let l = slant height of cone
Let r = radius of base of cone
height of cone, h = 24 cm
Volume of cone = 1232 cm³
$$\begin{gathered} \Rightarrow \frac{1}{3}\mathrm{\pi }\mathit{}{r}^2\mathit{}h=1232 \\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times \mathit{}{r}^2\times 24=1232 \\ \Rightarrow \mathit{}{r}^2=\frac{1232\times 7}{176} \\ \Rightarrow \mathit{}{r}^2=49 \\ \Rightarrow \mathit{}r\mathit{}=7\mathrm{cm} \\ \mathrm{Now},\mathrm{l}=\sqrt{r^2+\mathit{}{h}^2}=\sqrt{7^2+{24}^2}=\sqrt{49+576}=\sqrt{625}=25\mathrm{cm} \\ \mathrm{Curved}\mathrm{surface}\mathrm{area}=\mathrm{\pi }r\mathit{}l \\ =\frac{22}{7}\times 7\times 25 \\ =550{\mathrm{cm}}^2 \end{gathered}$$