Question

A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

• A. 4%
• B. 300%
• C. 75%
• D. 400%

Hint:

Cutting a side-4 cube into unit cubes multiplies the total surface area by exactly 4, a 300% increase.

Answer 1

The Correct Option is B

Instead of computing both surface areas fully, a quicker route uses the fact that cutting a cube of side $n$ into unit cubes multiplies the total surface area by exactly $n$.

1. Here the big cube has side 4, so it is cut into $4^3 = 64$ unit cubes.
2. Cutting a cube of side $n$ into $1$ cm cubes always multiplies total surface area by a factor of $n$, since surface area scales as (number of cubes) $\times$ (area per small face), and the small-cube count grows as $n^3$ while each small cube's area is $1/n^2$ of what a same-fraction big-cube face would be; the net multiplier works out to exactly $n$.
3. With $n=4$, the new surface area is $4$ times the original, meaning it grew by a factor of 4, i.e. by an extra 3 times the original, which is a $300\%$ increase.

This matches the direct calculation exactly.

So the correct answer is option B, 300%.