Question

The volume of a right circular cone is (100π) cm³ and its height is 12 cm. Find its slant height and its curved surface area.

Answer 1

Volume of the cone = (100π) cm³ and h = 12 cm

$$\begin{gathered} \therefore \frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h=100\mathrm{\pi } \\ \Rightarrow \frac{1}{3}{r}^2\times 12=100 \\ \Rightarrow r^2=\frac{300}{12}=\frac{100}{4} \\ \Rightarrow r=\sqrt{25}=5\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Now},l=\sqrt{r^2+h^2} \\ =\sqrt{5^2+{12}^2} \\ =\sqrt{25+144} \\ =\sqrt{169} \\ \Rightarrow l=13\mathrm{cm} \end{gathered}$$


$$\begin{gathered} \therefore \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cone}=\mathrm{\pi }rl\mathit{} \\ =\mathrm{\pi }\times 5\times 13 \\ =65\mathrm{\pi }{\mathrm{cm}}^2 \end{gathered}$$