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.

The large sphere has a diameter of 20 feet.

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.

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

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

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.

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

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.

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).