A vessel is in the form of a hollow hemisphere mounted by 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.
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AcademicMathematicsNCERTClass 10

Given:

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

To do:

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

Solution:

Diameter of the hemisphere $=14 \mathrm{~cm}$

This implies,

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

$=7 \mathrm{~cm}$

Curved surface area of the hemisphere $=2 \pi r^{2}$

$=2 \times \frac{22}{7} \times 7 \times 7$

$=308 \mathrm{~cm}^{2}$

Radius of the cylinder part $=$ Radius of hemisphere

$=7 \mathrm{~cm}$

Height of the cylinder $=$ Total height $-$ Radius of hemisphere

$=13-7$

$=6 \mathrm{~cm}$

Curved surface area of the cylinder $=2 \pi r h$

$=2 \times \frac{22}{7} \times 7 \times 6$

$=264 \mathrm{~cm}^{2}$

Total inner Surface area of the vessel $=$ Curved surface area of the hemisphere $+$ Curved surface area of the cylinder

$=308+264$

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

The inner surface area of the vessel is $572 \mathrm{~cm}^{2}$.

raja
Updated on 10-Oct-2022 13:24:32

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