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