A solid cube of side is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Step I: Finding side of the new cube
Side of the big solid cube
We know volume of a cube
So, Volume of the solid cube
Given that the solid cube is cut into small cubes of equal volumes.
Thus, Volume of each small cube
Let the side of small cube is
So the volume of a small cube
Thus, equating the volumes of the small cube, we get:
Thus, side of the new cube is .
Step II: Finding the ratio of surface areas.
We know, the Surface area of cube is given by
Surface area of the big solid cube of side
Surface area of the small cube of side
Ratio of of the cubes
Thus, the ratio of surface areas of two cubes is .