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Math Help - Mass of Ice Cream Cone using Triple Integrals

  1. #1
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    Mass of Ice Cream Cone using Triple Integrals

    Hey!
    I'm trying to find the mass of an ice cream cone made by 2 surfaces.
    The first is a sphere with radius 5 at the origin.
    The second is a cone centered around the positive z-axis emanating from the origin. The two intersect to make a circle of radius 3.
    The density is density= z mg/cm^3 (all dimensions were given in cm)

    Mainly I don't understand how to set the limits for the integration in terms of spherical.
    All help is greatly appreciated! Really stumped on where to begin.
    Last edited by ILoveTriangles; March 22nd 2012 at 10:22 PM.
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  2. #2
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    Re: Mass of Ice Cream Cone using Triple Integrals

    You're integrating z in a triple integral very like the first example here, Pauls Online Notes : Calculus III - Triple Integrals in Spherical Coordinates.

    So you'll have, int_0^(arcsin(3/5)) int_0^(2*pi) int_0^5 1/2 r^3 sin(2p) dr dt dp - Wolfram|Alpha

    And, just in case a picture helps for working through the triple from the inside out...




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  3. #3
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    Re: Mass of Ice Cream Cone using Triple Integrals

    If you look at the cone, it needs to have the equation z = \frac{4}{3}\sqrt{x^2+y^2} in order for its intersection with the sphere to be a circle with radius 3.
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