10. (10 pts) Find the flux of the vector field $\mathbf{F}$ on $\mathbb{R}^3$ defined by

$$\mathbf{F}=3x\mathbf{i}+2y\mathbf{j}+5z\mathbf{k}$$

through the surface $S=\left\{ \left(x,y,\sqrt{1-x^2-y^2}\right)\in\mathbb{R}^3 : x^2+y^2 \le 1 \right\}$ oriented with upward pointing normal vector field.

備註：$\mathbf{i}=(1,0,0),\ \mathbf{j}=(0,1,0),\ \mathbf{k}=(0,0,1)$.