Section 6.3
Geometry: Find the volume of the solid.
Radius = 3 units
Height = 4 units
What if we turn this cylinder on its side and make it really skinny?
Example: Rotate the function y = 3 between x = 2 and x = 6 about the x­axis and find the volume of the resulting solid.
Example: Volume of a solid of revolution by "slices"
the disk method
1. Sketch the region.
2.
Draw in one slice (rectangle) perpendicular to the axis of revolution.
3.
Sketch the solid obtained by revolving the region about the axis.
4.
Sketch the "slice" obtained by revolving this one rectangle...a disk.
5.
Write an expression for the volume of one slice.
6.
Find the exact volume by writing and evaluating a definite integral.
Example: Find the volume of the solid obtained by revolving the function f(x) around the x­axis.
[0, π]