Assignment:
Eight small cubes are put together to form one large cube. All six sides of the larger cube are painted, the paint is allowed to dry, and then the cube is taken apart.
a) How many of the small cubes will have paint on just one side? On two sides, On three sides? On no sides?
b) Complete the following table, assuming in turn that the large cube is formed from 27 and 64 cubes instead of eight.
c) Briefly explain the thinking and patterns you see. Explain.
Sides Painted Eight small cubes 27 small cubes 64 small cubes
one side
two sides
three sides
No sides
Provide complete and step by step solution for the question and show calculations and use formulas.