A cone and a cylinder of equal height have bases of equal radius. If the height of the cone is doubled and that of the cylinder is halved, what will be the ratio of their respective volumes?

Using the volume of a cone formula (one third pi times radius squared times height) and the volume of a cylinder formula (pi times radius squared times height), let the initial radius be r and initial height be h. After changing their dimensions, the new volume of the cone becomes two thirds pi times radius squared times height, and the new volume of the cylinder becomes half pi times radius squared times height. Dividing the new cone volume by the new cylinder volume gives a ratio of four to three.

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