(a) Set up a double integral for calculating the flux of the vector field $\vec{F}(x,y,z) = z^2 \vec{k}$ through the upper hemisphere of the sphere $x^2+y^2+z^2 = 4$, oriented away from the origin. If necessary, enter $\rho$ as rho, $\theta$ as theta, and $\phi$ as phi.

Flux = $\displaystyle \int_{A}^{B} \!\! \int_{C}^{D}$ $d\phi \, d\theta$

A =
B =
C =
D =

(b) Evaluate the integral.
Flux = $\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A}$ =

Hint: