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July 21st, 2017, 09:58 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 590 Thanks: 81  Is There A Proof Of This About The Volume Of Cones and Spheres?
Take a cone with equal radius and height, so the (r^2)h can be written as r^3. Based on the 4/3 and 1/3 coefficients in the volume formulas, a sphere with that radius will have four times the volume of the cone. Is there a proof that if you took four identical cones with equal radius and height and could make the material into whatever shape you wanted it could make a sphere with the same radius as each cone?

July 21st, 2017, 07:36 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 922 Thanks: 368 
I suspect there is a simple proof through integral calculus.

August 24th, 2017, 04:17 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
Assuming "conservation of volume", which is implied in your "make the material into whatever shape you wanted it", then the fact that the four cones have the same volume as the sphere is the proof. I don't know what more you could want.


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cones, proof, spheres, volume 
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