Question

The circumference of the base of a cone is 44 cm and its slant height is 25 cm. Find the volume and curved surface area of the cone.

Answer 1

Slant height, l = 25 cm
Circumference of the base of the cone = 44 cm

$$\begin{gathered} \mathrm{i}.\mathrm{e}.,2\mathrm{\pi }r\mathit{}=44 \\ \Rightarrow r\mathit{}=\frac{44}{2\mathrm{\pi }}=\frac{44\times 7}{2\times 22}=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Now},h=\sqrt{l^2-r^2}=\sqrt{{25}^2-7^2} \\ =\sqrt{625-49} \\ =\sqrt{576} \\ =24\mathrm{cm} \end{gathered}$$


$$\begin{gathered} \mathrm{Also},\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24 \\ =1232{\mathrm{cm}}^3 \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cone}=\mathrm{\pi }rl \\ =\frac{22}{7}\times 7\times 25 \\ =550{\mathrm{cm}}^2 \end{gathered}$$