Expert: Abe Mantell - 6/5/2005

Question
Hi Abe,

How would one go about finding the surface area of the sphere: x^2 + y^2 + z^2 = 4 that lies above the plane z=1?

Thanks so much,
Brandon

Answer
Hello Brandon,

There are a few ways...depending on how much math you know.
Are you in a calculus class?  Single or multi-variable?

I'll assume you are in a single-variable calculus class.

When z=1, the sphere intersects along the cirlce:
x^2+y^2=3 ==> a circle of radius sqrt(3)...
...so we can reduce this to finding the
surface area of the solid formed by rotating
x^2+y^2=4 about the x-axis, from x=1 to x=2.

Can you finish it from here?

Abe