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solids defined by cross sections. Those I've done. They're very cool.
You've got me ryos. I don't even know why you would bother using a third coordinate. It looks like the figure you have there can be described by boundaries in just the x and y axis. The way you are describing it, I don't even think that revolutions of solids is appropriate. Three dimensional calculus is seperate from what we are talking about here. The formula we are using here is derived based on a two dimensional analysis. I would dig into vector or multivariable calculus to solve it in the terms that you want to use.
And if you have a shape of known cross section, the integral becomes much simpler.
Yeah usually its pretty worthless but sometimes it can be usefull in drawing simple shapes quickly.
Really? Okay, I can play around with that. I haven't tried to much with paint even though it has been out forever. Honestly, I really never used it for much more than image manipulation, because the tools are soooo limited. I obviously am too cheap to go out and buy a decent software program. Thanks anyway.
lol. MS paint. I just drew two ellipses, connected the lines and filled in color to make it look how I wanted.
Yes you will and the formula I posted above multiplies the the average circumference of the rim by the change in arc length over that same distance. Note that like the disk or washer method for calculating volumes that the formula above rotates about the same axis as the variable!
this is what I'm seeing. If for instance you wanted to find the surface area of a sphere, sooner or later your gonna run into this piece:
Think of the arc length as a "height" and the circumference as a "width".
circumference times arclength. I figured it'd be something like that but how can that work? In some cases the arc portion is horizontal and has thickness. :-/
mikau, the integral for a surface of revolution is;
My book never discussed surface area of solids of revolution. I have a few idea's for how it might be accomplished but I've never tried. Maybe I should...
Try uploading the image again Ansette.
We have been given the problem of trying to find the minimum surface area given two variables in such a shape as the one in the image uploaded. any ideas?