Find the Volume: V = r2h = (242)(8) = 4608 in3 8 in 4 ft

Volume of Pyramids and Cones Geometry Mrs. Nakagawa

Objective To learn and use the formulas for finding the volumes of pyramids and cones.

Reminder: What is a Pyramid? Definition: A shape formed by connecting triangles to a polygon. Examples:

Reminder: What is a Cone? Definition: A shape formed from a circle and a vertex point. Examples: s

Volume Of A Cone. Consider the cylinder and cone shown below: D The diameter (D) of the top of the cone and the cylinder are equal. H The height (H) of the cone and the cylinder are equal. If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ? 3 times. This shows that the cylinder has three times the volume of a cone with the same height and radius. www.ltscotland.org.uk/Images/volumesofsolids_tcm4-123355.ppt

Formulas Volume of a Cylinder: V = r2 h Volume of a Cone: V= 1/3 pr2h

Example #1 Calculate the volume of: V= 1/3 pr2h V= 1/3 (p)(7)2(9) V = 147pm3

Example #2 Calculate the volume of: V= 1/3 pr2h V= 1/3 (p)(5)2(12) V = 100pcm3

Compare Compare a Prism to a Pyramid. Make a conjecture to what the formula might be for Volume of a Pyramid.

Formulas Volume of a Prism: Volume of a Pyramid: V = 1/3 Bh

Example #3 Calculate the volume of: V = 1/3 Bh V = 1/3 (102)(15) 15” V = 1/3 Bh V = 1/3 (102)(15) V = 500in3 10”

Volumes of Pyramids and Cones Homework Quizstar: Volumes of Pyramids and Cones