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1. The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The areas of inner curved surfaces of the vessels will be in the ratio of :

A. $\sqrt{2}$ : $\sqrt{3}$

B. 2 : 3

C. 4 : 9

D. 16 : 81

Solution:

Let their radii be R and r
Then,

\begin{aligned} \frac{\frac{2}{3} π R^{3}}{\frac{2}{3} π r^{3}} = \frac{6.4}{21.6} \\ \Rightarrow {(\frac{R}{r})}^{3} = \frac{8}{27} \\ \Rightarrow {(\frac{R}{r})}^{3} = {(\frac{2}{3})}^{3} \\ \Rightarrow \frac{R}{r} = \frac{2}{3} \end{aligned}

∴ Ratio of curved surface area :

= \frac{2 π R^{2}}{2 π r^{2}} = {(\frac{R}{r})}^{2} = \frac{4}{9} o r 4 : 9

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