Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram shows $AB$ as an arc of a circle centred at $O$ with radius $4\,\text{cm}$. The angle $AOB$ is $\alpha$ radians. Point $D$ lies on $OB$ so that $AD$ is perpendicular to $OB$. The arc $DC$, also centred at $O$, intersects $OA$ at $C$.
(i)[4]
Find an expression for the perimeter of the shaded region $ABDC$ in terms of $\alpha$.
(ii)[4]
Find the area of the shaded region $ABDC$ for the case where $\alpha = \frac{\pi}{6}$, and express your answer in the form $k\pi$, where $k$ is a constant to be determined.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Arc lengths $AB = 4\alpha$ and $DC = 4\alpha\cos\alpha$ are correct” …