Practice | Hashtable

1. The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is :

A. 2 : 3

B. 4 : 9

C. 12 : 9

D. None of these

Solution:

Let their edges be a and b
Then,

\begin{aligned} \frac{a^{3}}{b^{3}} = \frac{8}{27} \\ \Rightarrow {(\frac{a}{b})}^{3} = {(\frac{2}{3})}^{3} \\ \Rightarrow \frac{a}{b} = \frac{2}{3} \\ \Rightarrow \frac{a^{2}}{b^{2}} = \frac{4}{9} \\ \Rightarrow \frac{6 a^{2}}{6 b^{2}} = \frac{4}{9} O r 4 : 9 \end{aligned}

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