Lesson 5: Cavalieri's Principle and Volume of Composite Figures Answers

A three-dimensional model of Lucia’s apartment is shown. To cool the whole apartment, an air conditioner must provide 2.5 BTUs per cubic foot.

A pyramid with a rectangular base is stacked on top of rectangular prism. The height of the composite figure is 12 inches. The lengths of the rectangular base are 7 inches and 3 inches. The height of the rectangular prism is 4 inches.

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.

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).

The composite figure is made up of two congruent rectangular pyramids joined at their bases.

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.

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

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.