which of a papers has a greater surface area flat sheet of papaer or a crumpled sheet of paper?

The surface area of a sheet of paper is that two-dimensional boundary of the paper that is exposed to the outside surroundings.

For example: Assume the surface area of a sheet of paper of area size a is A = 2a because there are two distinct surfaces (e.g., front and back) exposed to the surroundings.

But now we fold the sheet into half. So now the surface area exposed to the surroundings is 1/2 a X 2 = a < A.

In other Words, by folding the paper in half we have reduced the surface area by one-half. If we simply extend that thought to include crumpling a piece of paper as meaning creating lots of folds it is reasonable to assume that the amount of area exposed to the outside will be reduced.

In other Words, the surface area of a crumpled piece of paper will be less than or equal to the same area of the uncrumpled piece. But generally and typically it will be less than the uncrumpled area. ANS