Question

From a cube measuring 5 inches on each edge, a one-inch cube us removed from the center of each face. The surface area of the resulting solid is what percent more than the surface area of the original cube? Record your answer as a percent, not decimal.

Answer 1

4%

Explanation:

The original cube has 6 faces, each with an area of 5^2 = 25 square inches. So the total surface area of the original cube is 6*25 = 150 square inches.

The one-inch cubes removed from the center of each face reduce the surface area of the cube by 6*1^2 = 6 square inches.

However, the removal of these cubes also creates 6 new square faces, each with an area of 1^2 = 1 square inch. So the surface area of the cube is increased by 6*1 = 6 square inches.

Therefore, the surface area of the resulting solid is 6 square inches more than the surface area of the original cube. This is a percentage increase of (6/150)*100% = 4%.

So the answer is 4

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