# Spherical coordinates prob

1. Oct 5, 2009

### likephysics

I need to brush up my math. I am trying to solve a spherical coordinates problem.
compute the divergence of the function
v=r cos$$\theta$$ r^ + r sin $$\theta$$ $$\theta$$^+ r sin $$\theta$$ cos $$\varphi$$ $$\varphi$$^
(r^ is r hat ...)
check the divergence theorem for this function, using as your volume the inverted hemisphere of radius R, resting on xy plane and centered at origin.

I couldn't find the surface area :
r is R
theta is from 0 to pi/2
phi is from 0 to 2pi

with constant R, surface area da = R^2 sin $$\theta$$ d$$\theta$$ d$$\varphi$$
How do I calculate the surface area of the hemisphere and the circle in the xy plane.
thanks.