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Surface Area and Volume of a Sphere

  1. Nov 12, 2013 #1
    I need to know the Surface Area and Volume of a spherical ball at the origin radius a.
    What I want is to evaluate the integrals at each integral.

    ##\oint_S dS =\int\int d? d? = 4 *\pi*r^2##

    ##\oint_V dV = \int_0^{\pi}\int_0^{2\pi}\int_0^a dr d\theta d\phi## = ##\frac{4}{3}*\pi*a^2##
    Last edited by a moderator: Nov 13, 2013
  2. jcsd
  3. Nov 13, 2013 #2


    Staff: Mentor

    Your last formula is incorrect: the volume of a sphere is ##(4/3)\pi r^3##.

    Also, you don't want closed path integrals - ordinary integrals will do just fine. For the surface area, you can do this with a single integral that represents the surface area of a surface of revolution, and for the volume, you can do this by calculating the volume of a solid of revolution
  4. Nov 13, 2013 #3


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    Science Advisor
    Gold Member

    The differential for surface area is dθsinφdφ with coefficient r2, for volume is r2drdθsinφdφ.
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