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.

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 cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.

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.

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

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.

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.

A cylinder is shown. A half-sphere is stacked on the top and the bottom of the cylinder. The diameter of the cylinder if 20 and the height of the cylinder is 28.