(i)[3]
Find a formula, in terms of $r$ and $\theta$, for the perimeter of the plate.
(ii)[3]
When $r = 10$ and $\theta = \frac{1}{5}\pi$, determine the area of the plate.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram shows a metal plate $OABC$, made up of a sector $OAB$ of a circle with centre $O$ and radius $r$, along with a triangle $OCB$ that is right-angled at $C$. Angle $AOB = \theta$ radians, and $OC$ is perpendicular to $OA$.