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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{557 cm}^{2}

{517 cm}^{2}

{537 cm}^{2}

{572 cm}^{2}

answer is D.

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Detailed Solution

Given that,
Diameter of the hemisphere is 14 cm.
Total height of the vessel is 13 cm.
Now,
Radius =

7

cm
Height of the cylindrical portion is

13 - 7 = 6

cm.
Curved surface area of cylindrical portion is =

2 πrh

\Rightarrow

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

\Rightarrow

{264 cm}^{2}

Curved surface area of hemispherical portion is =

2 π r^{2}

\Rightarrow

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

\Rightarrow

{308 cm}^{2}

Therefore, total surface area is

= 308 + 264

\Rightarrow {572 cm}^{2}

Hence, the correct option is 4.

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