Final answer:
When a piece of paper is rolled into a cylinder lengthwise, the height of the cylinder is the length of the paper. When the same piece of paper is rolled into a cylinder widthwise, the height of the cylinder is the width of the paper.
Step-by-step explanation:
When a piece of paper is rolled into a cylinder lengthwise, the length of the paper becomes the height of the cylinder and the width becomes the diameter of the cylinder. When the same piece of paper is rolled into a cylinder widthwise, the width of the paper becomes the height of the cylinder and the length becomes the diameter of the cylinder.
To compare the volumes, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where V is the volume, r is the radius, and h is the height. Since the radius is half the diameter, we can see that the height of the cylinder will be greater if the wider dimension of the paper is used.
Therefore, the piece of paper rolled into a cylinder widthwise will have a greater volume than the same piece of paper rolled into a cylinder lengthwise.