Solved Problem 09 | Cube

Let
$a$ = edge of smaller cube
$x$ = edge of smaller cube
 

Total area of smaller cube
$A_{small} = 6a^2$
 

Area of one face of the larger cube
$A_{large1} = x^2$
 

One face of larger cube = total area of smaller cube
$A_{large1} = A_{small}$

$x^2 = 6a^2$

$x = a\sqrt{6}$
 

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

Volume of larger cube
$V_{large} = x^3$

$V_{large} = (a\sqrt{6})^3$

$V_{large} = 6\sqrt{6} \, a^3$
 

Ratio of volumes

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

$= \dfrac{a^3}{6\sqrt{6} \, a^3}$

$= \dfrac{\sqrt{6}}{36}$           answer