If you cut a cube in half will the combined surface area of the two halves be more or less?

Answer 1

Yes it will be less because if you take a net of a cube and find the surface area it would be for example 30cm2 and if it was cut in half it would be 15cm squared so its smallerCORRECT ANSWER:Neither. It will be more in area because although you have made two halves of a cube, you have added a new exposed side on each of the halves, thus making 2 sides the same size as the cube. It will lessen by half the area on 4 of the sides which are bisected. So you get the same area that you started with. The above formula is close, but did not account for the other half.

Hooweestiki.

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THE ANSWERS ABOVE ARE WRONG.

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Here's why...

First, picture a cube one inch on a side.

Each side is one square inch; Six square inches total of SURFACE AREA .

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SCENARIO #1

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A slice (either vertical or horizontal) will add TWO (2) more sides, each being an additional square inch, for a sum total of eight (8) square inches.

An increase of 2 sq. in. over the original six (6) sq. in. is an increase of 33 percent. So, for vertical or horizontal halving, the formula is, as follows:

[ORIGINAL SURFACE AREA times 1.33]

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SCENARIO #2

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But if you halve the cube on a diagonal, the resultant new surfaces will be oblong, measuring 1" by 1.414" (the Square Root of two) adding almost another square inch of surface area.

2 x ( 1 x 1.414) = 2.828 square inches

The total SURFACE AREA is now 8.828 (when halved on the DIAGONAL).

This is an INCREASE of 47.13333 percent.

Resultant formula:

[ORIGINAL SURFACE AREA times 1.4713]

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THEREFORE

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FINALLY, the answer to your question is somewhere between these two extremes, because your cut will be neither a perfect vertical cut, nor a perfect diagonal cut.