The diagram shows a sector OBAC of a circle with centre O and radius 10 cm. The point P lies on OC and BP is perpendicular to OC. Angle AOC is \(\pi/6\) and the length of the arc AB is 2 cm.

(a) Find the angle BOC. [2]

(b) Hence find the area of the shaded region BPC giving your answer correct to 3 significant figures. [4]