AB Notes 5.6
Calculus AP
Volumes by Revolution
Practice sketching in the
3-D shapes on each of
these.
Name ___________________________
Video 1: Only watch the first 1:07 of the video. You should take down notes on the general
concept of finding volumes by the disc method as well as show all of the work for the specific
problem given. http://www.youtube.com/watch?v=7BKoBDF2My0 Links are on our website and
videos are Seckar-Martinez in the shared folder.
General Notes
Solve the Given Problem
Find the volume found by rotating y  x
around the x-axis on the interval [0,10].
Video 2: You will be solving two problems. Be sure to write lots of notes down.
http://www.youtube.com/watch?v=QYB0PFdXPyo Links are on our website and videos are SeckarMartinez in the shared folder.
Problem 1 – Disc Method
Problem 2 – Washer Method
3
The region bounded by y = 4x – x and the x-axis If the area bounded by the graphs of y  x
is in the first quadrant and is revolved about
and y = x is revolved about the x-axis, find the
the x-axis, forming a solid. What is the solid’s
volume of the resulting solid.
volume?
Video 3 – You will be solving another washer problem. http://patrickjmt.com/volumes-ofrevolution-diskwashers-example-1/ Links are on our website and videos are Seckar-Martinez in the
shared folder.
If the area bounded by the graphs of y = x3 and y = x is revolved about the x-axis, find the volume
of the resulting solid.
Video 4 - Trickier Washer Problem: http://patrickjmt.com/volumes-of-revolution-diskwashersexample-2/
Once you have your integral set up, you can use your calculator to get the final answer.
If the area bounded by the graphs of y = x3 and y = x is revolved about the line y = -2, find the
volume of the resulting solid. Sketch your own picture for this one.
If you finish early – play around with the applets on some of the following sites: Again – links are
on our website. HINT!!! Once you make the shape click on it and use your arrow keys to rotate the
object.
http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_16a.htm
http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2washer.htm
http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_18a.htm
http://higheredbcs.wiley.com/legacy/college/anton/0470183454/applets/ch6/figure6_2_13/washer_ex4.htm