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Help with Math Calculas

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the volume of a region bounded above by the unit sphere x^2+y^2+z^2=1 and below by the cone z=sqrt(x^2+y^2). I am really confuse here.. ><


    2. Relevant equations
    Sphere: x^2+y^2+z^2=1
    Cone: z=sqrt(x^2+y^2)

    3. The attempt at a solution
    I had plot the graph of the sphere and cone and i am pretty confuse to use. Just want to have some help.
     
  2. jcsd
  3. May 5, 2010 #2
    Volume requires a triple integral. How would you set this up? have you ever used polar/cylindrical/spherical coordinates?
     
  4. May 5, 2010 #3
    Tea, i try using polar coordinates..

    In the spherical, the equation of the sphere is r = 1

    And the cone is rcosθ=√(r^2 sin^2 θ cos^2 φ + r^2 sin^2 θ sin^2 φ)=rsinθ

    If we divide both sides by rcosθ, then we get

    tanθ=1,θ=π/4

    So, we have the triple integral:

    ∫0-2pi ∫0-(π/4) ∫0-1 (r^2 sinθdrdθdφ)

    I am not sure if this is correct..
     
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