Question

A cube of side 6 units is painted on all sides and then dissected into unit cubes.How many unit cubes are there with no side painted ?​

Answer 1

Answer:

Here is your ans

determine how many unit cubes would be painted on one or more sides. 36 (Side 1) + 30 (Side 2) + 50 (Total of Sides 3 and 4) + 20 (Side 5) + 16 (Side 6) = 152 sides painted.

216 - 152 = 64.

Another alternative solution would be to consider that all the outside unit cubes would be painted leaving the insides unpainted. Since you’re using unit cubes, this would be [6 - 2 (1)]^3 = 4^3 = 64.

Hope this helps