Question

The ratio between the lengths of the edges of two cubes are in the ratio $3:2.$ Find the ratio of their :
$\left(i\right)$ total surface areas
$\left(ii\right)$ volume.

Answer 1

Let the edges of a cube $1$ and cube $2$ be $x$ and $y$ respectively then $x:y=3:2$

$\left(i\right)$T.S.A of cube$1:$T.S.A of cube$2=\frac{6x^2}{6y^2}=\frac{x^2}{y^2}=\frac{3^2}{2^2}=9:4$

$\left(ii\right)$Volume of cube$1:$Volume of cube$2=\frac{x^3}{y^3}=\frac{3^3}{2^3}=27:8$