Cavalieri's Principle and Volume of Composite Figures Answers

A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown.

Cavalieri’s principle states that if two solids of equal height have equal cross-sectional areas at every level parallel to the respective bases, then the two solids have equal volume.The two shaded solids both have a height of 2r units. At every level, the areas of the cross sections of both solids equal π(r2 – b2).

A volleyball of radius 13 inches fits exactly in a cylinder with the same radius.

A rectangular prism with a square base is cut from the center of a triangular prism. Each side of the square base measures 1.7 units.

The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases.

A pyramid with a rectangular base is stacked on top of rectangular prism. The height of the composite figure is 10. The lengths of the rectangular base are 8 and 6 units. The height of the rectangular prism is 4.

The large sphere has a diameter of 20 feet.

A cone is stacked on top of a cylinder. They both share a circular base. The total height of the composite figure is 20. The height of the cylinder is 11 and the diameter is 12.

This composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units.