Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14cm$ and the total height of the vessel is $13cm.$ Find the inner surface area of the vessel.

Answer 1

The diameter of the hemisphere $=D=14cm$

The radius of the hemisphere $=r=7cm$

The height of the cylinder $=h=(13-7)=6cm$

The radius of the hollow hemisphere $=7cm$

The inner surface area of vessels $=$C.S.A of cylinder $+$ C.S.A of Hemisphere

$$\begin{gathered} =2\pi rh+2\pi r^2 \\ =2\pi r(h+r) \\ =2\times \frac{22}{7}\times 7\times (6+7) \\ =44\times 13 \\ =572c{m}^2 \end{gathered}$$

Hence, the inner surface area of the vessel is $572c{m}^2.$