Question

A cube of side 10 cm is painted blue on all six surfaces. Then it is cut into smaller cubes of side 1 cm each. How many of the smaller cubes will have blue paint on exactly two faces?

Answer 1

If the cube has a side of 10 cm, then it is a 10 by 10 by 10 cube.

The entirety of the surface area is painted blue, and it is then reduced to unit squares. What kinds of unit squares are there? There are the inside (0 blue) the face, (1 blue), the edge (2 blue), and the vertex (3 blue). In this question, we are trying to find the number of edge cubes, which is 10 (edge length) - 2(vertices at the end) = 8 (edge blocks in 1 edge)

8 x 12 (edges in a cube) = 96