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The diagram shows a metal plate \(O A B C\), consisting of a right-angled triangle \(O A B\) and a sector \(O B C\) of a circle with centre \(O\). Angle \(A O B = 0.6\) radians, \(O A = 6 \mathrm {~cm}\) and \(O A\) is perpendicular to \(O C\).
- Show that the length of \(O B\) is 7.270 cm , correct to 3 decimal places.
- Find the perimeter of the metal plate.
- Find the area of the metal plate.