1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Describing a Solid in Spherical Coordinates

  1. Nov 10, 2008 #1
    1. The problem statement, all variables and given/known data
    A solid lies above the cone [tex]z=\sqrt{x^2+z^2}[/tex] and below the sphere [tex]x^2+y^2+z^2=z[/tex]. Describe the solid in terms of inequalities involving spherical coordinates.

    2. Relevant equations
    In spherical coordinates, [tex]x=\rho\sin\phi\cos\theta[/tex], [tex]y=\rho\sin\phi\sin\theta[/tex], and [tex]z=\rho\cos\phi[/tex]

    3. The attempt at a solution
    I have no idea how to do this problem. My attempts have involved converting the two given equations to spherical coordinates, at which point everything is very messy and I don't know where to go next.

    I've attached a couple of 3D graphs to help with visualization.

    The answer is supposed to be [tex]0\leq\phi\leq\frac{\pi}{4}[/tex] and [tex]0\leq\rho\leq\cos{\phi}[/tex], but this doesn't make much sense to me.

    Any help would be great. Thanks!

    Attached Files:

    Last edited: Nov 10, 2008
  2. jcsd
  3. Nov 10, 2008 #2


    Staff: Mentor

    Shouldn't the equation of your cone be [tex]z = \sqrt{x^2 + y^2}[/tex]?
  4. Nov 10, 2008 #3


    User Avatar
    Science Advisor

    My recommendation is that you go back and read the problem again!

    You say "the cone [itex]z= \sqrt{x^2+ z^2}[/itex] is a complicated cylinder, not a cone. That may be why "everything is messy".

    I suspect it was really [itex]z= \sqrt{x^2+ y^2}[/itex]. In that case, the equation in spherical coordinates is [itex]r cos(\phi)= \sqrt{\rho^2 cos^2(\theta)sin^2(\phi)+ \rho^2 sin^2(\theta)sin^2(\phi)}= r sin(\phi)[/itex] which reduces to [itex]cos(\phi)= sin(\phi)[/itex]. It should be obvious that that reduces to [itex]\phi= \pi/4[/itex].
  5. Nov 10, 2008 #4
    Yes, this is correct. Thanks Mark!
  6. Nov 10, 2008 #5
    I didn't see how that reduced but I do now. Thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook