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 September 4th, 2017, 09:26 AM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Generic surface integral problem Find the centroid of the surface of a right circular cone of height h and base radius r, not including the base. I don't even know how to find the two variables gradient of ..
 September 4th, 2017, 09:42 AM #2 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 Nothing to do with gradient or surface integrals. Look up definition of centroid and take horizantal slices to get dA.
 September 4th, 2017, 09:48 AM #3 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 The official answer is on center axis, h/3 above the base But the google result is h/4 above the base Centriod of Right Circular Cone | Solved Example | Graphical Explanation | Engineering Intro
September 4th, 2017, 10:10 AM   #4
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Quote:
 Originally Posted by zollen The official answer is on center axis, h/3 above the base But the google result is h/4 above the base Centriod of Right Circular Cone | Solved Example | Graphical Explanation | Engineering Intro

where did you get this "official" answer and why is it "official" ?
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 September 4th, 2017, 12:09 PM #5 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 there is an area centroid and a volume centroid.
September 4th, 2017, 12:30 PM   #6
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The material answer. The question expects me to derive h/3 through surface integration.

Quote:
 Originally Posted by romsek where did you get this "official" answer and why is it "official" ?

Last edited by zollen; September 4th, 2017 at 12:35 PM.

 September 4th, 2017, 01:47 PM #7 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125 Because of symmetry, you just have to find z coordinate of centroid. For the surface: $\displaystyle \bar{z}=\frac{1}{A}\int_{A}zdA, \bar{z}=h/3$ for cone surface. For the volume: $\displaystyle \bar{z}=\frac{1}{V}\int_{V}zdV, \bar{z}=h/4$ for cone volume. Use horizantal slices to get dA or dV (elementary calculus). If you are dealing with masses, it's called cg. Ref: http://www.secs.oakland.edu/~latcha/...09-Finding.pdf Thanks from zollen Last edited by zylo; September 4th, 2017 at 02:40 PM.

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