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\includegraphics[max width=\textwidth, alt={}, center]{bb7595c9-93ae-49e8-9cc5-9ecc802e6060-10_593_841_260_651} The diagram shows a sector \(O B A C\) of a circle with centre \(O\) and radius 10 cm . The point \(P\) lies on \(O C\) and \(B P\) is perpendicular to \(O C\). Angle \(A O C = \frac { 1 } { 6 } \pi\) and the length of the \(\operatorname { arc } A B\) is 2 cm .

1. Find the angle \(B O C\).
2. Hence find the area of the shaded region \(B P C\) giving your answer correct to 3 significant figures. [4]