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July 20th, 2013, 09:26 AM   #1
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Finding Volume of a shape

Hi there,

I am trying to find volume of a shape which surface coordinates are depicted by this:

|x^n| + |y^n| + |z^n| = R^n


what I have come up to find volume is:

Volume = ??( R^n - |y^n| - |z^n|)^(1/n) dy dz (from 0 to R, from 0 to R) ? which should give 1/8 of total volume but it does not work.

Could you please comment and explain me, why it does not work.

Any help is appreciated.
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July 21st, 2013, 04:04 AM   #2
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Re: Finding Volume of a shape

How can you get 1/8? The volume should be functioned to n and R.
KyVanchhay is offline  
July 21st, 2013, 06:00 AM   #3
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Re: Finding Volume of a shape

power 11110 is not saying that the volume is 1/8, he is saying that since the absolute values make the integrand symmertric about the 8 octants, it is sufficient to do this for x, y, and z all positive to get 1/8 of the entire volume.

If , and all of x, y, and z are positive, then, of course, .

Now, if x= 0, we have and so when z= 0, so that y= R. That is, y goes from 0 to R and, for each y, z goes from 0 to .

The total volume will be .

As for actually doing that integral- you are on your own!
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July 22nd, 2013, 03:19 AM   #4
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Re: Finding Volume of a shape

Sorry. I didn't understand what he was saying. Thanks, Hallsoflvy.
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