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Home > CALC > Chapter 8 > Lesson 8.1.5 > Problem 8-51
Using the methods you have learned, find the volume of the region bounded by:
-axis After sketching an arbitrary rectangle (with
), it is apparent that there will not NOT be a hole in the center of this solid.
That indicates that the Disk Method will be appropriate.-axis This arbitrary rectangle indicates that there will be a hole in the center of this solid. You will have to use the Washer Method.
Horizontal rectangles indicate that the bounds and the integrand will be in terms of
. Notice that the figure will be a cylinder with a curvy hole in the center.
The radii of the cylinder is.
The radii of the curvy hole is. Q: Washers or disks? Think: Will there be a hole or won't there?
Q: Will the integral be in terms of
or ? Think: Are the rectangles vertical or horizontal? Notice that these radii are
units longer than the radii in part (b).