Question

A cube of side 4 $cm$ is cut into cubes of side 1 $cm$. Calculate the total surface area of all the small cubes.

• A. $262c{m}^2$
• B. $460c{m}^2$
• C. $484c{m}^2$
• D. $384c{m}^2$

Answer 1

The correct option is D

$384c{m}^2$

Side of original cube = 4 $cm$.

Number of cubes of side 1 $cm$
$=\frac{Volumeofbiggercube}{Volumeofsmallercube}$
$=\frac{4\times 4\times 4}{1\times 1\times 1}$
$=64$

Now, surface area of one cube
$=6(side{)}^2$
$=6\times (1{)}^2$
$=6\times 1$
$=6c{m}^2$

$\therefore$ surface area of 64 cubes
$=6\times 64c{m}^2$
$=384c{m}^2$

Hence, total surface area of all the small cubes is $384c{m}^2$.