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The diagram shows a sector \(A O B\) of a circle, centre \(O\) and radius \(r \mathrm {~cm}\). Angle \(A O B\) is \(72 ^ { \circ }\).
- Express \(72 ^ { \circ }\) exactly in radians, simplifying your answer.
The area of the sector \(A O B\) is \(45 \pi \mathrm {~cm} ^ { 2 }\).
- Find the value of \(r\).
- Find the area of the segment bounded by the arc \(A B\) and the chord \(A B\), giving your answer correct to 3 significant figures.