(a)[2]
Show that $\angle PCS = \frac{2}{3}\pi$ radians.
(b)[3]
Find the exact perimeter around the plate.
(c)[5]
Show that the area of the plate is $\left(\frac{20}{3}\pi + 8\sqrt{3}\right)\text{ cm}^2$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram illustrates a symmetrical metal plate. It is formed by cutting out two congruent parts from a circular disc with centre $C$. The outline of the plate is made up of the two arcs $PS$ and $QR$ from the original circle, together with two semicircles having $PQ$ and $RS$ as diameters. The radius of the circle with centre $C$ is $4\text{ cm}$, and $PQ = RS = 4\text{ cm}$ as well.