2.2: Concentric sectors with a shaded strip

0606/21/M/J/18 — Question 6 · 7 marks

2.2 diagram
In the diagram AOBAOB and DOCDOC are sectors of a circle centre OO. The angle AOBAOB is xx radians. The length of the arc ABAB is 40 cm40\text{ cm} and the radius OBOB is 16 cm16\text{ cm}.
(i)
Find the value of xx.
[2]
(ii)
Find the area of sector AOBAOB.
[2]
(iii)
Given that the area of the shaded region ABCDABCD is 140 cm2140\text{ cm}^2, find the length of OCOC.
[3]