Question

The circumference of the base of a cone is $\frac{220}{7}$ cm and its slant height is 13 cm. Find the volume of the cone. $\left(\mathrm{\pi }=\frac{22}{7}\right)$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cone},l=13\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{be}r\mathrm{and}h,\mathrm{respectively}. \\ \mathrm{As},\mathrm{the}\mathrm{circumference}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{220}{7}\mathrm{cm} \\ \Rightarrow 2\mathrm{\pi }r=\frac{220}{7} \\ \Rightarrow 2\times \frac{22}{7}\times r=\frac{220}{7} \\ \Rightarrow \frac{44r}{7}=\frac{220}{7} \\ \Rightarrow r=\frac{220\times 7}{7\times 44} \\ \Rightarrow r=5\mathrm{cm} \\ \mathrm{Also}, \\ h=\sqrt{l^2-r^2} \\ =\sqrt{{13}^2-5^2} \\ =\sqrt{169-25} \\ =\sqrt{144} \\ =12\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ =\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 12 \\ =\frac{2200}{7}{\mathrm{cm}}^3 \end{gathered}$$