Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a circle of radius $r$ cm with centre $O$. $A$ and $B$ are points on the circumference, and $ABCD$ is a rectangle. The angle $AOB = 2\theta$ radians, and $AD = r$ cm.
(i)[3]
Express the perimeter of the shaded region using $r$ and $\theta$.
(ii)[4]
In the case where $r = 5$ and $\theta = \frac{\pi}{6}$, find the area of the shaded region.
(c(ii))[4]
In the case where $r = 5$ and $\theta = \frac{1}{6}\pi$, find the area of the shaded region.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finds $AB = 2r\sin\theta$ or a matching equivalent expression” …