What's the relation between the curved surface area of a hemisphere and the total surface area of hemisphere?

C S A = \frac{2}{3} \times T S A

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C S A = \frac{3}{2} \times T S A

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T S A = \frac{2}{3} \times C S A

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C S A = \frac{4}{3} \times T S A

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Solution

The correct option is A $C S A = \frac{2}{3} \times T S A$
We know that,
Total surface area of hemisphere of radius 'r' $= 3 π r^{2}$
Curved surface area of the hemisphere of radius 'r' $= 2 π r^{2}$

Now,
$C S A = T S A \times x$
$\Rightarrow 2 π r^{2} = 3 π r^{2} \times x$
$\Rightarrow \frac{2}{3} = x$

$∴$ For a hemisphere of radius 'r',
CSA = $\frac{2}{3} \times$ TSA

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