1.6: Sector area, arc length and segment area

0606/11/O/N/18 — Question 5 · 7 marks

1.6 diagram
The diagram shows a circle with centre OO and radius r cmr\text{ cm}. The minor arc ABAB is such that angle AOBAOB is θ\theta radians. The area of the minor sector AOBAOB is 48 cm248\text{ cm}^2.
(i)
Show that θ=96r2\theta = \dfrac{96}{r^{2}}.
[2]
(ii)
Given that the minor arc ABAB has length 12 cm12\text{ cm}, find the value of rr and of θ\theta.
[3]
(iii)
Using your values of rr and θ\theta, find the area of the shaded region.
[2]