# Spherical shape surface area calculation

## Homework Statement ## 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