(a) Calculate the flux of the vector field $\vec{F}(x,y,z) = 3 \vec{i} - 7 \vec{k}$ through a sphere of radius $5$ centered at the origin, oriented outward.
Flux =

(b) Calculate the flux of the vector field $\vec{F}(x,y,z) = \vec{i} - 3 \vec{j} + 8 \vec{k}$ through a cube of side length $5$ with sides parallel to the axes, oriented outward.
Flux =

Hint: