Question

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

Answer 1

Let their edges be $a$ and $b$.
Then
$\Rightarrow$ $\frac{a^3}{b^3}$ =$\frac{8}{27}$

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

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

Now,

$\Rightarrow$ $\frac{a^2}{b^2}$ = $\frac{4}{9}$

$\Rightarrow$ $\frac{6a^2}{6b^2}$ = $\frac{4\times 6}{9\times 6}$

$\Rightarrow$ $\frac{6a^2}{6b^2}$ = $\frac{4}{9}$

Ratio of their surface area is $4:9$