11-4 Volumes of Prisms and Cylinders. Rotation, Length, Area There are four different types of measurement in geometry. Three of these are… ROTATION:

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11-4 Volumes of Prisms and Cylinders

Rotation, Length, Area There are four different types of measurement in geometry. Three of these are… ROTATION: Angle, in degrees

Rotation, Length, Area There are four different types of measurement in geometry. Three of these are… LENGTH: Distance between points, measured in inches, feet, meters…

Rotation, Length, Area There are four different types of measurement in geometry. Three of these are… AREA: How big a region is, measured in square feet, etc.

The fourth measure: Volume The volume of a solid is the number of cubic units contained in its interior. Volume is measured in cubic units, such as cubic meters (m 3 ) or cubic feet.

MEASUREMENTS Rotation: Angles, in degrees Length/Distance: Feet, meters, etc. Area: Square feet, square meters, etc. Volume: Cubic feet, cubic meters, etc.

Volume of a Prism The volume of a prism is the product of the area of the base and the height of the prism. V = Bh

Finding the Volume of a Prism What is the volume of the rectangular prism?

 What is the volume of the rectangular prism?

 What is the volume of the triangular prism?

Volume of a Cylinder The volume of a cylinder is the product of the area of the base and the height of the cylinder. V = πr 2 h

Finding the Volume of a Cylinder What is the volume of the cylinder in terms of π?

Cavalieri’s Principle If two prisms have the same base and the same height, they have the same volume, even if one is “tilted”. Compare: All parallelograms with the same base and height have the same area, regardless of their “tilt”.

 What is the volume of the cylinder at the right in terms of π?