Cavalieri's Principle and Volume of Composite Figures Answers

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 large sphere has a diameter of 20 feet.

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.

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.

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

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

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

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

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