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.)

Quote:

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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.)

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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.

Quote:

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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.

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

Good Job Kittycat!

This is my 34:):)th post!!!

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! ;) :)
I really appreciate your effort!:)

Quote:

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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! ;) :)
I really appreciate your effort!:)

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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