Question

Clare takes a piece of paper, cuts it in half, then stacks the pieces. She takes the stack of two pieces, then cuts in half again to form four pieces, stacking them. She keeps repeating the process. What is the area in square inches of each piece?

A) 1 square inch
B) 2 square inches
C) 4 square inches
D) 8 square inches

Answer 1

The area of each piece of paper remains the same after continuously cutting and stacking, and is a fraction of the original paper's area. Without knowing the initial area, we can't specify the exact area in square inches for each piece from the provided options.

Step-by-step explanation:

When Clare continuously cuts the paper in half and stacks the pieces, the area of each piece remains constant because she is dividing the paper into smaller but equal parts. The initial area of the paper is not specified, so we cannot determine the exact area in square inches for each piece after cutting. However, if we are to assume that the initial piece of paper had an area that was a whole number, then the area will always be an equal fraction of the original, thus remaining a whole number if divided evenly. Given the options provided (1, 2, 4, 8 square inches), without knowing the original size, we cannot definitively choose one of these options as each could be correct depending on the original size of the paper. The area of a piece of paper does not change based on the number of pieces stacked, only the thickness of the stack changes.