If the volumes of two cubes are in the ratio $8: 125$, then the ratio of their surface areas is :\

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Professor PC Thomas Classes · Answer

(b) : Let $a$ be side of one cube and $b$ be side of another cube.\ Given, ratio of their volumes $=8: 125$\ $\Rightarrow \frac{a^{3}}{b^{3}}=\frac{8}{125} \Rightarrow\left(\frac{a}{b}ight)^{3}=\left(\frac{2}{5}ight)^{3} \Rightarrow \frac{a}{b}=\frac{2}{5}$\ Ratio of their surface are $=\frac{6 a^{2}}{6 b^{2}}=\left(\frac{a}{b}ight)^{2}=\left(\frac{2}{5}ight)^{2}=$ i.e., $4: 25$\