Final answer:
The ratio of the volumes of a cone and a cylinder with the same height and radius is 1:3, as the volume of the cone is one-third of the cylinder's volume.
Step-by-step explanation:
The student asked whether the ratio of volumes of a cone and a cylinder depends only on their heights, their radii, or if the volumes are equal when both the height and radius are the same.
The correct option is D: The volumes are equal when the height and radius are the same. This is because the formula for the volume of a cylinder is V = πr²h, and the formula for the volume of a cone is V = ⅓πr²h. When you have a cone and a cylinder with the same height (h) and radius (r), the volume of the cone will be one-third of the volume of the cylinder. Therefore, the ratio of their volumes depends on both their heights and radii, but when these dimensions are identical, the volume of the cone is exactly one-third that of the cylinder.