125 small cubes like the one below are arranges to make a larger cube. How many small cubes make up the width?

1 Answer
Feb 16, 2018

5

Explanation:

I am assuming 125 identical cubes with edge length#s# are stacked to build a larger cube.

Hmm...

Using the fact that #V=s^3#, the volume of the smaller cube is #s^3#.

Now, if we stack 125 of them, the volume of the larger cube is #125s^3#

Also, the larger cube has an edge length #S#.

Using this, we see that #V=S^3=125s^3#

We can now solve this to find #S# in terms of #s#.

=>#S^3=125s^3#

=>#S=root [3] (125s^3)#

=>#S=root [3] (5^3*s^3)#

=>#S=5s#

This tells us that the edge length of our larger cube has to be 5 times the length of the edge length of our smaller cube.

If we were trying to compose the larger cube with smaller cubes, 5 shorter edges have to be put together take the place of one longer edge.

Therefore, 5 cubes make up the width.