Let S Be the Oriented Upwards $z=100-x^{2}-y^{2}, z \geq 0$

Multiple Choice

Let S be the oriented upwards. Use a computer surface $z=100-x^{2}-y^{2}, z \geq 0$ algebra system to find the rate of mass flow of a fluid of density $\rho$ through $S$ if the velocity field is given by $\mathbf { F } ( x , y , z ) = 0.5 z k$ .

A) $25,000 \pi \rho$
B) $5,000 \pi \rho$
C) $25 \pi \rho$
D) $250,000 \pi \rho$
E) $2,500 \pi \rho$