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 <x,y,z>.. 
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  
Senior Member Joined: Sep 2015 From: USA Posts: 2,505 Thanks: 1374  Quote:
where did you get this "official" answer and why is it "official" ?  
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 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 
The material answer. The question expects me to derive h/3 through surface integration. 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/...09Finding.pdf Last edited by zylo; September 4th, 2017 at 02:40 PM. 

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