Question

A cube of side $5$ cm is cut into $1$ cm cubes. What is the ratio of surface areas of original cube and cut out cube?

• A. $5:1$
• B. $25:1$
• C. $50:1$
• D. None

Answer 1

The correct option is B $25:1$

Let the side of original cube$=x_1=5$ cm

Surface area of original cube $=A_1=6{x_1}^2$

$\therefore A_1=6\times 5^2=6\times 25c{m}^2$

Now, length of side of new cube $=x_2=1$ cm

Surface area of new cube $=A_2=6{x_2}^2$

$\therefore A_1=6\times 1^2=6\times 1=6c{m}^2$

$\therefore \frac{A_1}{A_2}=\frac{6\times 25}{6}=\frac{25}{1}$

$\therefore A_1:A_2=25:1$

So, option B is correct.