A mechanical component for a precision pendulum clock is designed using a triangular metal plate OAB OAB\,OAB attached to a weighted circular sector OBC OBC\,OBC with centre OOO.
In this design:
Determine the size of angle OABOABOAB, giving your answer in radians to 4 significant figures.
Calculate the area of the triangular plate OAB OAB\,OAB in cm2\text{cm}^2cm2, giving your answer to 3 significant figures.
Given that the ratio of the area of the weighted sector OBC OBC\,OBC to the area of the triangular plate OAB OAB\,OAB is 7:4 7:4\,7:4
Show that angle BOC BOC\,BOC is 0.224 radians to 3 significant figures.
Hence find the total perimeter of the component, in cm, to the nearest integer.
