Question

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone.

Answer 1

Let h cm be the height of cone and l cm be its slant height.
Radius of the sphere=5 cm
Radius of the cone = 4 cm

Now, surface area of the sphere = 5(Curved surface area of the cone)
$$\begin{gathered} 4\mathrm{\pi }\times 5^2=5\times (\mathrm{\pi }\times 4\times l) \\ l=5\mathrm{cm} \\ \mathrm{Hence},\mathrm{height}h=\sqrt{l^{\mathit{2}}\mathit{-}{r}^2}=\sqrt{25-16}=\sqrt{9}=3\mathrm{cm} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }\times 4^2\times 3 \\ =\frac{22\times 16}{7} \\ =50.3{\mathrm{cm}}^3 \end{gathered}$$