Question

Ratio of surface areas of two cubes is $25:36$. Find the ratio of their volumes.

Answer 1

Surface area of cube $6x^2$

$\frac{surfacearea1stcube}{surfacearea2ndcube}=\frac{25}{36}$

$\frac{6a^2}{6b^2}=\frac{25}{36}\Rightarrow \frac{a}{b}=\sqrt{\frac{25}{36}}$

i. e $\frac{a}{b}=\frac{5}{6}=5:6$

volume of cube $x^2$

$\frac{volumeof1stcube}{volumeof2ndcube}=\frac{a^3}{b^3}$

$\frac{a^3}{b^3}=\frac{5^3}{6^3}=\frac{125}{216}$

$\therefore$ Ratio of volume

$=125:216$