Question

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

Answer 1

Answer:

So lets say the side length of the original cube is 'a'.

Now the volume of the original cube is equal to

and the surface area of the original cube

If the cube is cut into 27 identical cubes then the volume of each cube is:

where,  is the side length of each smaller cube. So, the surface area of each tiny cube is:

Now, there are 27 identical cubes so the total surface area is:

Now, the surface area of the original cube is

and surface area of 27 identical cubes is

So, the percentage increase in the total surface area is:

Percentage increase , where N stands for new value, O stands for the old value.

So the percentage increase in the total surface area is 200%.