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Bell Work: Find the Volume: V = r 2 h = (24 2 )(8) = 4608 in 3 4 ft 8 in

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Volume of Pyramids and Cones

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

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

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

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Volume Of A Cone. Consider the cylinder and cone shown below: The diameter (D) of the top of the cone and the cylinder are equal. D D The height (H) of the cone and the cylinder are equal. H H 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.

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Formulas Volume of a Cone: V= 1/3 r 2 h Volume of a Cylinder: V = r 2 h

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Example #1 Calculate the volume of: V= 1/3 r 2 h V= 1/3 ( )(7) 2 (9) V = 147 m 3

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Example #2 Calculate the volume of: V= 1/3 r 2 h V= 1/3 ( )(5) 2 (12) V = 100 cm 3

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

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

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Example #3 Calculate the volume of: 10” 15” V = 1/3 Bh V = 1/3 (10 2 )(15) V = 500in 3

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Homework Work Packet: Volumes of Pyramids and Cones

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