A large cube has a volume of 1 cubic unit. A small cube has a volume of 1 27 of a cubic unit. What is the difference between the edge length of the large cube and the edge length of the small cube?

Given:

Volume of Large cube = 1 cubic unit

Volume of small cube = cubic unit

To find:

The difference between the edge length of the large cube and the edge length of the small cube.

Solution:

Let the edges of large and small cubes are and respectively.

We know that, volume of a cube is

Volume of Large cube = 1 cubic unit

Taking cube root on both sides, we get

So, edge of large cube is 1 unit.

Volume of small cube = cubic unit

Taking cube root on both sides, we get

So, edge of large cube is unit.

Now, difference between them is

Therefore, the difference between the edge length of the large cube and the edge length of the small cube is unit.