Cavalieri's Principle and Volume of Composite Figures Answers

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

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 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 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.

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.

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

Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.