help in finding volume

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morteza08
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help in finding volume

cross section area of this body is a circle with radius R. and the cones at the ends are the same.. write down a procedure to calculate the volume based on h.
0<h<2R

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

Re: help in finding volume

cross section area of this body is a circle with radius R. and the cones at the ends are the same.. write down a procedure to calculate the volume based on h. 0<h<2R
The shape in the middle is a cylinder on its side; the cylinder has length L and radius R; you only need the area of the curved sides (not the "end caps"). The shapes on the end are cones with radius R and height d; you only need the area of the curved sides (not the bases). But what exactly is "h" measuring? I'm not sure??

morteza08
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Re: help in finding volume

in the routine derivation of the volume of cone by integration ,
http://commons.wikimedia.org/wiki/File: ... RATION.pdf

http://en.wikibooks.org/wiki/Calculus/Volume

it means you have a circular base with the constant radius of R and integrate along the height d(as in the current problem).. in fact we are summing up the volumes of discs along height with the base area of pi*r*r and this must be multiplied by the delta(d) and then we integrate this along height from o to d..

in ths case i am going to keep the height as condstant and integrate along radius... we have some cones that put above each other...
I hope I can explain clearly.

morteza08
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Joined: Wed Aug 20, 2014 9:46 am
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Re: help in finding volume

oh oh
Excuse me buddy..
I didn't ask the exact problem as is..
My question is . suppose this is a water reservoir...
calculate the volume of this reservoir based on h... I mean if we fill the reservoir with water , up to h. how we calculate the volume.

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

Re: help in finding volume

Okay. So this isn't geometry; it's calculus. And you're not doing anything standard like finding the volume of a cylinder in a nice orientation; you're finding the partial volume of a complicated shape in a not-nice orientation. That was important information. (Admin/mods: Please move this to "calculus".)

You can see lots of Q-and-A's on the Ask Dr. Math site. There's a long discussion with two worked examples in this article. And you may be able to check your work by using this calculator. If you get stuck, please write back showing what you've done so far. Thanks.