# Homework Help: Surface integral help.

1. Feb 22, 2010

1. The problem statement, all variables and given/known data
What is the area of the portion of the sphere $$x^{2}+y^{2}+(z-a)^{2}=a^{2}$$ that is inside the paraboloid $$z=x^{2}+y^{2}$$

2. Relevant equations
$$\int\int_{S} dS$$

3. The attempt at a solution

I used this

$$\int\int_{S} dS=\int\int_{R}\sqrt{f^{2}_{x}+f^{2}_{y}+1}dx dy$$

And got

$$=\int\int_{R}\frac{a}{\sqrt{a^{2}-x^{2}-y^{2}}}dx dy$$

I know that R is the projection of the surface on the xy plane, but I tried a few different ways to compute the boundaries but it never made sense. Maybe I'm just approaching it the wrong way. Anyone can help me with this?

2. Feb 22, 2010

### Gib Z

Can you please show us what you tried? Did you try solving for the bounds algebraically? Draw a diagram to aid you, and solve the equations simultaneously.