Solved Problem 08 | Cube

Let
$a$ = edge of the smaller cube, thus,
$a\sqrt{3}$ = edge of the larger cube
 

Volume of the smaller cube
$V_{small} = a^3$
 

Volume of the larger cube
$V_{large} = (a\sqrt{3})^3$

$V_{large} = 3\sqrt{3} \, a^3$
 

Required ratio

$= \dfrac{V_{small}}{V_{large}}$

$= \dfrac{a^3}{3\sqrt{3} \, a^3}$

$= \dfrac{\sqrt{3}}{9}$           answer