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

Given:

A vessel in the form of a hollow hemisphere mounted by a hollow cylinder.

The diameter of the hemisphere is \( 14 \mathrm{~cm} \) and the total height of the vessel is \( 13 \mathrm{~cm} \).

To do:

We have to find the inner surface area of the vessel.

Solution:

Diameter of the hollow hemisphere $= 14\ cm$

This implies,
Radius of the hemisphere $=\frac{14}{2}$

$ = 7\ cm$

Total height of the vessel $=13\ cm$

Height of the cylindrical part $=13-7$

$= 6\ cm$

Therefore,

Inner surface area of the vessel $=$ Inner surface area of the cylindrical part $+$ Inner surface area of the hemispherical part

$=2 \pi r h+2 \pi r^{2}$

$=2 \pi r(h+r)$

$=2 \times \frac{22}{7} \times 7(6+7)$

$=2 \times 22 \times 13$

$=572 \mathrm{~cm}^{2}$

The inner surface area of the vessel is $572\ cm^2$.

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Updated on: 10-Oct-2022

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