The ratio of the surface areas of two hemispheres is $4 : 1$ . What is the ratio of their volumes?

8 : 1

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4 : 1

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3 : 1

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2 : 1

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Solution

The correct option is A $8 : 1$
S.A. of hemisphere $= 2 π r^{2}$
$∴ \frac{S . A .1}{A . A . 2} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{4}{1} \Rightarrow \frac{r_{1}}{r_{2}} = 2$
$∴ \frac{V_{1}}{V_{2}} = \frac{2 \frac{π}{3} r_{1}^{3}}{\frac{2 π}{3} r_{2}^{3}} = {(\frac{r_{1}}{r_{2}})}^{3} = 8$

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