Ratio of surface areas of two cubes is $1 : 25$ . Find the ratio of their voulmes.

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Solution

Surface area of cube $= 6 {S i d e}^{2}$
Volume of cube $= {S i d e}^{3}$

Let sides of the two cubes be $a, b$ respectively
Ratio of surface areas of two cubes is $1 : 25$
$⟹ 6 a^{2} : 6 b^{2} = 1 : 25$
$a : b = 1 : 5$
Ratio of their volumes is $a^{3} : b^{3} = 1^{3} : 5^{3} = 1 : 125$

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