Surface area of sphere above xy-plane within a cylinder

[mathwurkz]

Hi! I don't know how to approach this problem. I need a little bit of help please. Here is the problem:
Find the surface area of that portion of the sphere $$x^2 +y^2 + z^2 =a^2$$ that is above the xy-plane and within the cylinder $$x^2 + y^2 = b^2, 0 \leq b \leq a$$

 

[whozum]

Give us some input on the integral youre thinking about..

 

[saltydog]

Hi! I don't know how to approach this problem. I need a little bit of help please. Here is the problem:
Find the surface area of that portion of the sphere $$x^2 +y^2 + z^2 =a^2$$ that is above the xy-plane and within the cylinder $$x^2 + y^2 = b^2, 0 \leq b \leq a$$

Two things Mathwurkz:

1. That's not a surface integral but rather a calculation to determine the surface area. Surface integrals are different. Check them out if you wish.

2. Draw a picture: Ideally, draw one in 3-D using Mathematica or other software. But even a cross section would be helpful. Once you have an accurate picture in mind, it's easier to construct the integral for the surface area.

Edit: One more thing Mathwurkz:

What happens when a=b? Then the problem is easy right? Anyway, that's a good way to check your integration: If it works for this simple case which is known by inspection, then that gives some confidence it's correct when b is less than a.