Question

A solid cube of side $12$ cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Answer 1

Given:

Side $12$cm

$\Rightarrow$Volume of cube $=12\times 12\times 12=1728$cm${}^3$

$\Rightarrow$Volume of smaller cube

$=\frac{1}{8}$ of $1728$
$=\frac{1}{8}\times 1728=216$cm${}^3$

$\Rightarrow$Let side be $S$.
$\therefore$ $({S)}^3=216$
$\Rightarrow$$S=6$ cm

Ratio of SA of cubes

$=\frac{\text{SA of bigger cube}}{\text{SA of smaller cube}}$

$={\left(\frac{12}{6}\right)}^2=\frac{2^2}{1}=\frac{4}{1}$

$\therefore$ Ratio between their surface areas $4:1$