Volume: The Disk Method. Some examples of solids of revolution:

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Presentation transcript:

Volume: The Disk Method

Some examples of solids of revolution:

Volume: The Disk Method If a region in the plane is revolved about a line, the resulting solid is a solid of revolution.

Volume: The Disk Method When we put these disks together, we get a solid.

Volume: The Disk Method

Ex:Find the volume of the solid of revolution by rotating about the x-axis to the line x = 9. x = 9 (0, 0)

Volume: The Disk Method Ex:Find the volume of the solid of revolution by rotating the region formed by y = 3 – x 2 and y = 2 about the line y = 2. y = 2 y = 3 – x 2 (–1, 2) (1, 2)

Ex:Find the volume of the solid of revolution by rotating the bounded region formed by f (x) = x 3, the y-axis, and y = 8 about the y-axis. Volume: The Disk Method y = 8 f (x) = x 3 (0, 0) (2, 8)