Question

A cube with an edge length of 4 inches is painted on all of its sides. Then the cube is cut into 64 cubes with an edge length of 1 inch. What percent of the total surface area is painted? Explain.

Answer 1

Please refer to the diagrams to understand these answers:

CUBE (1):

Paint on cube (1) contains 3.125% of the paint.

CUBE (2):

Paint on cube (2) contains 2.083% of the paint.

CUBE (3):

Paint on cube (3) contains 1.042% of the paint.

CUBE (4):

Contains 0% of the paint.

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There would be four different types of cubes which would contain different amounts of paint.

Some cubes in fact would have no paint (cube (4)). Now we can check if our results are correct by counting how many cube (1)'s, cube (2)'s, cube (3)'s and cube (4)'s there are...

Cube (1) x 8 + Cube (2) x 24 + cube (3) x 24 + cube (4) x 8

= 3.125% x 8 + 2.083% x 24 + 1.042% x 24 + 0% x 8

= 1

= 100%