Cavalieri's Principle and Volume of Composite Figures Answers

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.

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 large sphere has a diameter of 20 feet.

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

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.

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