A cube of edge length 6 cm is sliced into 20 congruent pieces by vertical cuts perpendicular to a base of the cube and parallel to a face. The total surface area of the 20 pieces exceeds the surface area of the original cube by x square centimeters. What is x? (Do NOT include punctuation in your answer.)

The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.

Step-by-step explanation:

The formula of surface area for the entire cube (), measured in square centimeters, is:

(Eq. 1)

Where is the side length, measured in centimeters.

If this cube is sliced into 20 pieces, the surface area of each slice (), measured in square centimeters, is equal to:

(Eq. 2)

And the surface area of all slices (), measured in square centimeters, is:

(Eq. 3)

Then, we calculate the excess of surface area (), measured in square centimeters, by applying the following formula:

(Eq. 4)

If , then the excess of surface area is:

The total surface area of the 20 pieces exceeds the surface area of the original cube by 1368 square centimeters.

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