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Spherical shape surface area calculation

  1. Oct 12, 2014 #1
    1. The problem statement, all variables and given/known data
    upload_2014-10-12_13-3-58.png

    2. Relevant equations

    Surface area of sphere = 4*Pi*r^2, where r: is the radius of the sphere circle


    3. The attempt at a solution
    Solution:


    1. In terms of “r” and “R”, and the radius of sphere “S”, and “d”:

    Given that:

    · Surface area of both shaded area are equal: That means,

    The area bounded by P, A (outside Q) = the area bounded by N&M, A (N&M), while,

    The area bounded by P = the area outside Q, A (outside Q), then

    A (outside Q) = A (N&M)

    And for the surface area bounded by N&P “A (N&P) “

    A (N&P) = the whole area of the sphere S “A (S) “–[A (outside Q) + A (inside Q) + A (N&M)],

    And for, A (N&M) = A (outside Q), then,

    A (N&P) = A (S) – [2*A (outside Q) + A (inside Q)]

    Knowing that the surface area formula of sphere “A sphere” = 4*Pi*r^2

    Where Pi = 3.143, and r: the radius of the sphere circle

    · given that the radius of the sphere is “S”, then,

    ØA (S) = 4*Pi*S^2

    · given that the radius of the sphere Q is “r”, then

    ØA (inside Q) = 4*Pi*r^2.

    A (outside Q) =

    Dear Sirs here,

    As you see its a problem of getting the surface area of irregular shape which you had seen in the previous image,

    Expecting that you took a look at my attempt solving the problem, and understood how i prepared the equation to get the bounded surface area between curves N&M, having those small red curves with the available given data,

    what i need the help for, is that the area outside the sphere Q which is limited by the curve P, " i used symbol for it of A (outside Q)" and those red small curves, is how i get the equation which calculates that area win terms of "r", "S", "d" and "R"?, or any of these parameters, and then later i optimize the equation to be in terms of those parameters

    Looking forward to hear from you, and will appreciate your help, i have been using physics forums for many years ago, and putting a big hope in here to get the help

    Thanks

     
  2. jcsd
  3. Oct 17, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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