If a cube with the length of the side of 4 cm is cut into smaller cube

A cube has 6 faces.

The surface area of a cube with the length of the side of 4 cm is \(6*4^2=6*16\) \(cm^2\).

Now, since the volume of the big cube is \(4^3=64\) \(cm^3\) and the volume of the smaller cubes is \(1^3=1\) \(cm^3\), then when the big cube is cut into the smaller cubes we'll get \(\frac{64}{1}=64\) little cubes. Each of those little cubes will have the surface area equal to \(6*1^2=6\) \(cm^2\), so total surface are of those 64 little cubes will be \(6*64\) \(cm^2\).

\(6*64\) is 4 times more than \(6*16\) which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): \(\text{Percent} = \frac{\text{Change}}{\text{Original}}*100\)

So the percent increase will be: \(Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*64-6*16}{6*16}*100=300%\).


Answer: D