July 20th, 2013, 09:26 AM  #1 
Newbie Joined: Jul 2013 Posts: 1 Thanks: 0  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. 
July 21st, 2013, 04:04 AM  #2 
Member Joined: May 2013 From: Phnom Penh, Cambodia Posts: 77 Thanks: 0  Re: Finding Volume of a shape
How can you get 1/8? The volume should be functioned to n and R.

July 21st, 2013, 06:00 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 5  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! 
July 22nd, 2013, 03:19 AM  #4 
Member Joined: May 2013 From: Phnom Penh, Cambodia Posts: 77 Thanks: 0  Re: Finding Volume of a shape
Sorry. I didn't understand what he was saying. Thanks, Hallsoflvy.


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