Spherical shape surface area calculation

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SUMMARY

The discussion focuses on calculating the surface area of a spherical shape, specifically addressing the equation for the surface area of a sphere, given by the formula A = 4*Pi*r^2, where r is the radius. The user attempts to derive the surface area of an irregular shape bounded by various curves and seeks assistance in formulating an equation that expresses the area outside sphere Q in terms of parameters r, S, d, and R. The user emphasizes the need for clarity in the equations and the relationships between the areas defined in the problem.

PREREQUISITES
  • Understanding of spherical geometry and surface area calculations
  • Familiarity with the mathematical constant Pi (π)
  • Knowledge of algebraic manipulation of equations
  • Experience with curve analysis in geometry
NEXT STEPS
  • Research the derivation of surface area formulas for irregular shapes
  • Learn about the application of calculus in calculating areas bounded by curves
  • Explore geometric relationships involving multiple spheres and their surface areas
  • Investigate optimization techniques for geometric equations
USEFUL FOR

Students studying geometry, mathematicians focusing on surface area calculations, and anyone involved in solving complex geometric problems related to spheres and irregular shapes.

gaber2611
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Homework Statement


upload_2014-10-12_13-3-58.png


Homework Equations


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

The Attempt at a Solution


Solution:[/B]

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

 
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