Find the volume of the solid obtained by rotating the region bounded by , , and about
Chapter 6, Problem 6.62(choose chapter or problem)
Find the volume of the solid obtained by rotating the region bounded by , , and about the -axis. SOLUTION The region is shown in Figure 7(a) and the resulting solid is shown in Figure 7(b). Because the region is rotated about the y-axis, it makes sense to slice the solid perpendicular to the y-axis and therefore to integrate with respect to y. If we slice at height y, we get a circular disk with radius x, where . So the area of a crosssection through y is and the volume of the approximating cylinder pictured in Figure 7(b) is Since the solid lies between y 0 and y 8, its volume is
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer