Question

The radius of the base of a cone is 14 cm and its height is 24 cm. Find the volume, curved surface area and the total surface area of the cone.

Answer 1

Here, r = 14 cm and h = 24 cm

Volume of the cone = $\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h$
$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times 14\times 14\times 24 \\ =4928{\mathrm{cm}}^3 \end{gathered}$$

Curved surface area of the cone = $\mathrm{\pi }rl$
$$\begin{gathered} =\frac{22}{7}\times 14\times \sqrt{7^2+{24}^2} \\ =22\times 2\times 25 \\ =1100{\mathrm{cm}}^2 \end{gathered}$$

∴ Total surface area of the cone = $\mathrm{\pi }rl\mathit{}+\mathrm{\pi }{r}^2$
$$\begin{gathered} =1100+\frac{22}{7}\times 14\times 14 \\ =1100+616 \\ =1716{\mathrm{cm}}^2 \end{gathered}$$