How much will the surface area increase if the cube is cut in half?

First, picture a cube one inch on a side.

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

-------------------

SCENARIO #1

-------------------

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]

-------------------

SCENARIO #2

-------------------

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]

-------------------

THEREFORE

-------------------

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.