Mathematics 9709 · AS & A Level · Circular measure

Circular measure — practice question

In the diagram, $ACB$ is a semicircle with centre $O$ and radius $r$, and arc $OC$ belongs to a circle centred at $A$.
(i)[1]

Express angle $CAO$ in radians as a multiple of $\pi$.

(ii)[4]

Find the area of the shaded region, giving your answer in terms of $r$, $\pi$ and $\sqrt{3}$ in simplest form.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: The correct angle is $\angle CAO=\frac{\pi}{3}$

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