Question

Two cubes have their volumes in the ratio 8:27. The ratio of their curved surface area is:

Answer 1

Let the Sides of cube be $a,b$

Volume of cubes are given by $a^3,b^3$

Ratio of Volumes is given by $a^3:b^3=8:27$

${\left(\frac{a}{b}\right)}^3={\left(\frac{2}{3}\right)}^3$

$\frac{a}{b}=\frac{2}{3}$

$a=\frac{2}{3}b$

The surface area of Cubes is given by $6a^2,6b^2$

$=6a^2:6b^2$

$=a^2:b^2$

Put $a=\frac{2}{3}b$

$={\left(\frac{2}{3}b\right)}^2:b^2$

$=\frac{4}{9}:1$

$=4:9$