Question

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

Answer 1

Given that the vessel is formed by mounting a hollow hemisphere of diameter $14cm$ on a hollow cylinder. The height of the vessel is $13cm$.

Consider the above figure based on the given information.

To find out: Inner surface area of the vessel.

Height of the hemisphere $=$ radius of hemisphere $=\frac{14}{2}$

$=7cm$

Hence, height of cylinder $\left(h\right)=$ height of vessel $-$ height of hemisphere

$\Rightarrow h=13-7$

$=6cm$

Now, inner surface area of vessel $=$ C.S.A. of Hemisphere $+$ C.S.A. of cylinder

We know that,

C.S.A. of hemisphere $=2\pi r^2$

C.S.A. of cylinder $=2\pi rh$

$\therefore$ Inner surface area of vessel $=2\pi r(r+h)$ $[2\pi r^2+2\pi rh]$

$\Rightarrow 2\times \frac{22}{7}\times 7(7+6)$ $[\because \pi =\frac{22}{7}]$

$\Rightarrow 2\times 22\times 13$

$\Rightarrow 572c{m}^2$

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