# spherical coordinates -triple integral

• Sep 12th 2007, 07:22 AM
kittycat
spherical coordinates -triple integral
find the volume of the ice cream cone G cut from the solid sphere rho < or = 1 by the cone phi = pi/3.

Please teach me how to find the limits of the variable for this question especially for rho.

Thank you very much.

Note: I think theta should be from 0 to 2pi.
phi should be from 0 to pi/3.
rho should be from 0 to 1. ( Intuitively, i think rho is from 0 , if I am right, I would like to have your opinion why rho is from 0.)
• Sep 12th 2007, 07:56 AM
ThePerfectHacker
Quote:

Originally Posted by kittycat
find the volume of the ice cream cone G cut from the solid sphere rho < or = 1 by the cone phi = pi/3.

Please teach me how to find the limits of the variable for this question especially for rho.

Thank you very much.

Note: I think theta should be from 0 to 2pi.
phi should be from 0 to pi/3.
rho should be from 0 to 1. ( Intuitively, i think rho is from 0 , if I am right, I would like to have your opinion why rho is from 0.)

It seems correct. The only possible mistake here is the limits on phi. Because if the whole angle from side to side is pi/3 then phi is half that, i.e. pi/6. But if phi is measured from the axis of symettry to its side then you use phi to pi/3. But I do not know if this what it asks.
• Sep 12th 2007, 09:48 AM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
It seems correct. The only possible mistake here is the limits on phi. Because if the whole angle from side to side is pi/3 then phi is half that, i.e. pi/6. But if phi is measured from the axis of symettry to its side then you use phi to pi/3. But I do not know if this what it asks.

phi is measured from the axis of symmetry, so it's ok.

Good Job Kittycat!

This is my 34:):)th post!!!
• Sep 12th 2007, 05:05 PM
kittycat
Hi Jhevon,

Nice to hear from you again. Could you please explain to me why rho is from 0 to 1? I want to hear your opinion about the range of rho especially why it starts from 0.

This is my 34:):)th post!!!
Your are a great teacher with a lot of contribution to this forum! ;) :)
• Sep 12th 2007, 05:41 PM
Jhevon
Quote:

Originally Posted by kittycat
Hi Jhevon,

Nice to hear from you again. Could you please explain to me why rho is from 0 to 1? I want to hear your opinion about the range of rho especially why it starts from 0.

This is my 34:):)th post!!!
Your are a great teacher with a lot of contribution to this forum! ;) :)