the following figures all have the same height and same base area. for which of the figures can we apply…

Explanation:

Step1: Recall Cavalieri's principle

Cavalieri's principle states that if two solids have the same height and the same cross - sectional area at every level parallel to the bases, then they have the same volume.

Step2: Analyze the cross - sectional areas of the given figures

For a pyramid (A), a cone (B), and a cylinder (C) with the same height and base area, at every level parallel to the bases, the cross - sectional areas of the pyramid and the cone are proportional to the square of the distance from the vertex, and the cross - sectional area of the cylinder is constant. But for two solids with the same height and base area, a pyramid and a cone have the same cross - sectional area at the same height above the base. A cylinder has a different cross - sectional area property compared to the pyramid and the cone. So we can apply Cavalieri's principle to the pyramid and the cone.

Answer:

A. Only A and B