2.5: Sector arc length and segment area

0606/22/M/J/16 — Question 6 · 7 marks

2.5 diagram
The diagram shows a sector of a circle with centre OO and radius 5 cm5\text{ cm}. The length of the arc ABAB is 7 cm7\text{ cm}. Angle AOBAOB is θ\theta radians.
(i)
Explain why θ\theta must be greater than 11 radian.
[1]
(ii)
Find the value of θ\theta.
[2]
(iii)
Calculate the area of the sector AOBAOB.
[2]
(iv)
Calculate the area of the shaded segment.
[2]