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November 30th, 2012, 01:56 PM   #1
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Volume of intersection of cylinders

The axes of two right circular cylinders of radius interstect at a right angle. Find the volume of the solid of intersection of the cylinders.

Why radius is , well, I don't know.
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November 30th, 2012, 02:01 PM   #2
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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:

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November 30th, 2012, 03:27 PM   #3
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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
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November 30th, 2012, 05:02 PM   #4
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Re: Volume of intersection of cylinders

Quote:
Originally Posted by etidhor
And could you solve this problem? http://mymathforum.com/viewtopic.php?f=13&t=36334
Sorry, homework not done here.
Please show your work: we can then tell you where you're wrong. Thank you.
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December 1st, 2012, 02:24 AM   #5
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Re: Volume of intersection of cylinders

Quote:
Originally Posted by MarkFL
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:

Where is pi??? I think u solution is incorrect, yesterday while i was in bed i solved this problem in my brain and answer had pi in it
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December 1st, 2012, 02:39 AM   #6
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Re: Volume of intersection of cylinders

Since the cross-sections are square, there is no pi. The solution I gave is correct.
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December 1st, 2012, 03:17 AM   #7
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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.
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December 1st, 2012, 03:20 AM   #8
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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
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December 1st, 2012, 06:46 AM   #9
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Re: Volume of intersection of cylinders

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Originally Posted by MarkFL
Sorry, you are right, I got it, I just don't believe anything unless solid proof is brought.
What about this problem: http://mymathforum.com/viewtopic.php?f=13&t=36334?
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December 1st, 2012, 09:44 AM   #10
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Re: Volume of intersection of cylinders

Now can anyone explain how did Archimedes calculated it without calculus? ...
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