Question

Question:
A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

Answer 1

Solution:

When a 5 cc cube is sliced into 1 cc cubes, we will get 5*5*5 = 125 1 cc cubes.

In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.

Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.

In each face of the larger cube, there will be 5*5 = 25 cubes. Of these, there will be 16 cubes on the edge and 3*3 = 9 cubes which are not on the edge.

Therefore, there will be 9 1-cc cubes per face that will have exactly one of their sides painted.

In total, there will be 9*6 = 54 such cubes.

Answer 2

Answer⤵️

A 5 cm^3 cube divided in 1cm^3 cubes = 125 cubes in total. A cube has 6 faces.

On each face, all the cubes surrounding the boundary will have more than 1 side painted, which makes total of 5+5+3+3 = 16 cubes.

So we are left with 25-16 = 9 cubes on each face (which has only 1 side painted)totaling to 9*6=54 cubes.

Answer is 54..

Hope this helps...✨