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

25%

Step-by-step explanation: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?

Find the surface area of the painted cube.

6(42) = 96 in2.

Find the surface area of each of the smaller cubes.

6(12) = 6 in2.

Find the total surface area of the smaller cubes.

64(6) = 384 in2.

Find the percent of the total surface area painted.

96

384

= 0.25, or 25%.

The total surface area painted is 25%.

Answer 2

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%