A right cone has a base with diameter 10 units. The volume of the cone is \(100\pi\) cubic units. What is the length of a segment drawn from the apex to the edge of the circular base?

A right pyramid has a square base with sides of length 10 units. Each segment connecting the apex to a midpoint of a side of the base has length 13 units. What is the volume of the pyramid?

For each pair of solids, determine if their volumes are the same or different. If the volumes are different, identify the solid with the greatest volume. Explain your reasoning.

1. A prism and a pyramid have the same height. The pyramid’s base has 3 times the area of the prism's base.
2. A pyramid and a cylinder have bases with the same area. The cylinder’s height is 3 times that of the pyramid.
3. A cone and a cylinder have the same height. The cone’s radius is 3 times the length of the cylinder’s radius.