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November 30th, 2012, 12:56 PM  #1 
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Volume of intersection of cylinders
The axes of two right circular cylinders of radius æ interstect at a right angle. Find the volume of the solid of intersection of the cylinders. Why radius is æ, well, I don't know. 
November 30th, 2012, 01:01 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Volume of intersection of cylinders
We can use slicing to find the volume of the resulting solid. If we choose an axis z perpendicular to the two axes of symmetry of the intersecting cylinders of radii r, we find square cross sections, whose side lengths s are , thus the volume V is: 
November 30th, 2012, 02:27 PM  #3 
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Re: Volume of intersection of cylinders
Answer is correct. I understood that you wrote all stuff to get correct answer. But thanks for explanation. And could you solve this problem? http://mymathforum.com/viewtopic.php?f=13&t=36334 
November 30th, 2012, 04:02 PM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,688 Thanks: 701  Re: Volume of intersection of cylinders Quote:
Please show your work: we can then tell you where you're wrong. Thank you.  
December 1st, 2012, 01:24 AM  #5  
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Re: Volume of intersection of cylinders Quote:
 
December 1st, 2012, 01:39 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Volume of intersection of cylinders
Since the crosssections are square, there is no pi. The solution I gave is correct.

December 1st, 2012, 02:17 AM  #7 
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Re: Volume of intersection of cylinders
Dude it can't be square, the intersection will be spherical cube, 'I couldn't remember exact word for it' just use math software to draw it, and you will see.

December 1st, 2012, 02:20 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Volume of intersection of cylinders
I googled it, and found these: http://www.math.tamu.edu/~tkiffe/cal...2cylinder.html http://mathworld.wolfram.com/SteinmetzSolid.html 
December 1st, 2012, 05:46 AM  #9  
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Re: Volume of intersection of cylinders Quote:
What about this problem: http://mymathforum.com/viewtopic.php?f=13&t=36334?  
December 1st, 2012, 08:44 AM  #10 
Member Joined: Nov 2012 Posts: 50 Thanks: 0  Re: Volume of intersection of cylinders
Now can anyone explain how did Archimedes calculated it without calculus? ...


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cylinders, intersection, volume 
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