Question

A solid cube of side $12$ cm is cut into eight cubes of equal volume. The side of the new cube and the ratio between the surface areas of the two cubes respectively are:

• A. $6$cm, $5:1$
• B. $4$cm, $4:1$
• C. $6$cm, $4:1$
• D. $5$cm, $6:1$

Answer 1

The correct option is C $6$cm, $4:1$

Given, A solid cube is of side $12$ cm.

Volume of solid cube$={\left(12\right)}^3=1728c{m}^3$

Let edge of each small cube$=a$ cm

Number of small cubes$=8$

Now, $1728=8\times a^3$

$\Rightarrow a^3=216$

$\Rightarrow a=\sqrt[3]{3216}=6cm$

$\therefore$ Edge of each small cube$=6cm$

Now, $\frac{\text{Surface area of solid cube}}{\text{Surface area of small cube}}=\frac{6\times {\left(12\right)}^2}{6\times {\left(6\right)}^2}=\frac{144}{36}=4:1$