1. ## Visualize This...

The base of S is a circular disk with a radius r. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.

Does somebody have some good graphing software who can help me visualize this thing? In my mind, circular disk is also called a cylinder, and you can get a square from a cross section depending on where you cut it, but only if you cut it in exactly the right place. Clearly I am missing something.

Thanks.

2. ## Re: Visualize This...

closest I could find ...

link to a Quicktime animation of square cross sections with an elliptical base ...

http://www.mathwords.com/assets/movi...onsExample.mov

3. ## Re: Visualize This...

Thanks for that. I need to watch that one a few times.

4. ## Re: Visualize This...

Originally Posted by joatmon
The base of S is a circular disk with a radius r. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.

Does somebody have some good graphing software who can help me visualize this thing? In my mind, circular disk is also called a cylinder
No, a "circular disk" is NOT called a cylinder. A cylinder is a three dimensional object while a "circular disk" is a two dimensional object- a circle and its interior.

, and you can get a square from a cross section depending on where you cut it, but only if you cut it in exactly the right place. Clearly I am missing something.
Yes, because of your mistaken idea that we are talking about a cylinder. Imagine a circle with square erected on top of it.

Thanks.

And here is the next problem...

The base of S is a circular disk with a radius r. Parallel cross sections perpendicular to the base are isosceles triangles with height h and unequal side in the base. Find the volume of the solid. Somebody shoot me.

5. ## Re: Visualize This...

立体的平行截面 - calculus的日志 - 网易博客

6. ## Re: Visualize This...

Thanks. This is what drives me nuts about these types of problems. You say that a "circular disk" is a two dimensional object. After studying this problem for a long time, I agree with you that this problem does use the term in that way. But in the normal world, a two dimensional object with circular properties has a more generally accepted name - a circle! A disk is ALWAYS three dimensional (except in a calculus textbook).

Why can't they just say that the object has a circular base? Doing the math is one thing, but if you have to "decode" their unnecessarily misleading descriptions before you can do that, it wastes time that I just don't have. (as does me complaining about it).

"Imagine a circle with a square erected on top of it". Unfortunately, I'm not a drug user...

Thanks for your help, though. I appreciate it.