# Thread: spherical coordinates -triple integral

1. ## 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.)

2. 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.

3. 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 34th post!!!

4. 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 34th post!!!
Your are a great teacher with a lot of contribution to this forum!
I really appreciate your effort!

5. 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 34th post!!!
Your are a great teacher with a lot of contribution to this forum!
I really appreciate your effort!
well, rho does start from 0 because the cone reaches to the origin. what is the distance from the origin to the tip of the cone that is at the origin? 0 of course. the cone is a solid figure that passes through the origin, so rho will be from zero to something