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Find the curved surface area (CSA) of the hemisphere if the volume is $2425 \frac{1}{2} m^{3}$

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693 m^{2}

692 m^{2}

653 m^{2}

593 m^{2}

answer is A.

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Detailed Solution

Given, volume of hemisphere

= 2425 \frac{1}{2} {cm}^{3}

= \frac{485}{2} {cm}^{3}

Suppose the radius of the hemisphere be '

r

cm

.
Now, Volume of hemisphere

= \frac{2}{3} π r^{3}

\Rightarrow \frac{2}{3} π r^{3} = \frac{4851}{2}

\Rightarrow \frac{2}{3} \times \frac{22}{7} \times r^{3} = \frac{4851}{2}

\Rightarrow r^{3} = \frac{4851 \times 3 \times 7}{2 \times 2 \times 22}

\Rightarrow r^{3} = \frac{441 \times 21}{2 \times 2 \times 2}

\Rightarrow r^{3} = \frac{21 \times 21 \times 21}{2 \times 2 \times 2}

\Rightarrow r = \sqrt{3} \frac{21 \times 21 \times 21}{2 \times 2 \times 2}

\Rightarrow r = \frac{21}{2} cm \dots \dots \dots \dots \dots (1)

So, Curved surface area of hemisphere

CSA = 2 π r^{2}

Put value “r” from equation (1),

CSA = 2 \times \frac{22}{7} \times {(\frac{21}{2})}^{2}

= 2 \times \frac{22}{7} \times \frac{21 \times 21}{2 \times 2}

= 693 {cm}^{2}

Correct option is 1.

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