11.6 Volume of Prisms and Cylinders Mrs. vazquez Geometry

G-gmd.1.1, 1.3-4 Essential Question: How does Cavalieri’s Principle relate with a stack of coins? Objective: Students will be able to calculate volume of prisms and cylinders.

postulates Volume of a Cube Post.: The volume of a cube is the cube of the length of its side. Volume ≅ Post.: If two polyhedra are ≅, then they have the same volume. Volume (+) Post.: The volume of a solid is the sum of the volumes of all its nonoverlapping parts.

theorems Volume of a Prism: The volume of a prism is V = Bh, where B is the area of a base & h is the height. Volume of a Cylinder: The volume of a cylinder is V = Bh = πr2h, where B is the area of a base, h is the height, & r is the radius of the base.

Cavalieri’s principle If two solids have the same height & the same cross- sectional area at every level, then they have the same volume.