Question

A cube of side $4cm$ is cut into $1cm$ cubes.

What is the ratio of the surface areas of the original cubes and cut-out cubes?

• A. $1:2$
• B. $1:3$
• C. $1:4$
• D. $1:6$

Answer 1

The correct option is C

$1:4$

Explanation for the correct answer:

We know that, when we make one shape from the other shape, then their volume is equal. then,

$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{small}\mathrm{cubes}=\frac{\mathrm{volume}\mathrm{of}\mathrm{bigger}\mathrm{cube}}{\mathrm{Volume}\mathrm{of}\mathrm{small}\mathrm{cube}}$

The number of small cubes $=\frac{4^3}{1^3}\Rightarrow 64$

Now,

$Surfaceareaofbiggercube=6a^2$

Surface area of bigger cube $=6\times 4^2\Rightarrow 96c{m}^2$

$Surfaceareaofsmallercube=6a^2$

Surface area of smaller cube $=6\times 1^2\Rightarrow 6c{m}^2$

Now, $Surfaceareaof64smallercubes=64\times 6=384c{m}^2$

So,

$Requiredratio=\frac{Surfaceareaofbiggercube}{Surfaceareaof64smallercubes}=\frac{96}{384}=\frac{1}{4}=1:4$

Hence, option (C) is correct.