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September 4th, 2017, 09:26 AM   #1
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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 <x,y,z>..
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September 4th, 2017, 09:42 AM   #2
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Nothing to do with gradient or surface integrals. Look up definition of centroid and take horizantal slices to get dA.
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September 4th, 2017, 09:48 AM   #3
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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
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September 4th, 2017, 10:10 AM   #4
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Quote:
Originally Posted by zollen View Post
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
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there is an area centroid and a volume centroid.
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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.

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Originally Posted by romsek View Post

where did you get this "official" answer and why is it "official" ?

Last edited by zollen; September 4th, 2017 at 12:35 PM.
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September 4th, 2017, 01:47 PM   #7
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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
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Last edited by zylo; September 4th, 2017 at 02:40 PM.
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