Question

The height of a cone is 21 cm and its slant height is 28 cm. The volume of the cone is
(a) 7356 cm³
(b) 7546 cm³
(c) 7506 cm³
(d) 7564 cm³

Answer 1

(b) 7546 cm³

$$\begin{gathered} \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cone},r=\sqrt{l^2-h^2} \\ =\sqrt{{28}^2-{21}^2} \\ =\sqrt{784-441} \\ =\sqrt{343}\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{1}{3}\times \frac{22}{7}\times 343\times 21 \\ =22\times 343 \\ =7546{\mathrm{cm}}^3 \end{gathered}$$