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The area of the hemisphere is $100 m^{2}$ . Find its volume. (Use $π = 3.14$ ).

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132.97 m^{3}

102.97 m^{3}

112.97

c m^{3}

122.97 m^{3}

answer is A.

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Detailed Solution

Given that, the area of the hemisphere =

100 m^{2}

.
The formula for the area of hemisphere is given by,
Area of hemisphere

= 2 π r^{2}

So, after substituting the value of all the dimensions in the formula we get,

\Rightarrow 100 = 2 \times 3.14 \times r^{2}

\Rightarrow \frac{100}{(2 \times 3.14)} = r^{2}

\Rightarrow r = \sqrt{15.923}

\Rightarrow r = 3.99

m
The formula for the volume of hemisphere is given by,
Volume of the hemisphere, V

=

\frac{2}{3} π r^{3}

So, after substituting the value of all the dimensions in the formula we get,

V = \frac{2}{3} \times 3.14 \times 3.99 \times 3.99 \times 3.99

\Rightarrow V = 132.97 m^{3}

Therefore, the volume of hemisphere is

132.97 m^{3}

.
Hence option (1) is correct.

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