2. Given the radius of the base of a cylinder is $r$, and the height is $h$. If the volume of the cylinder is 1, and the surface area is 12, then $\frac{1}{r}+\frac{1}{h}=$ ( ).
(A) 2
(B) 3
(C) 6
(D) 12
2. C.

From the given equations, we have
$$
\pi r^{2} h=1,2 \pi r^{2}+2 \pi r h=12 \text {. }
$$

Dividing the two equations yields $\frac{1}{r}+\frac{1}{h}=6$.