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On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.

Paul
August 7, 2018

Calculus I - Practice Problems
 Integrals Previous Chapter Next Chapter Extras Volumes of Solids of Revolution/Method of Cylinder Previous Section Next Section Work

More Volume Problems

1. Find the volume of a pyramid of height h whose base is an equilateral triangle of length L. [Solution]

2. Find the volume of the solid whose base is a disk of radius r and whose cross-sections are squares.  See figure below to see a sketch of the cross-sections.

[Solution]

3. Find the volume of the solid whose base is the region bounded by  and  and whose cross-sections are isosceles triangles with the base perpendicular to the y-axis and the angle between the base and the two sides of equal length is .  See figure below to see a sketch of the cross-sections.

[Solution]

4. Find the volume of a wedge cut out of a “cylinder” whose base is the region bounded by ,  and the x-axis.  The angle between the top and bottom of the wedge is .  See the figure below for a sketch of the “cylinder” and the wedge (the positive x-axis and positive y-axis are shown in the sketch  they are just in a different orientation).

[Solution]

Problem Pane
 Volumes of Solids of Revolution/Method of Cylinder Previous Section Next Section Work Integrals Previous Chapter Next Chapter Extras

[Notes]

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