(a)[3]
Show that the metal plate has area $r^2(\pi + \theta)$.
(b)[4]
Show that the perimeter of the metal plate does not depend on $\theta$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a metal plate $OABCDEF$ made up of $3$ sectors, all with centre $O$. Sector $COD$ has radius $2r$ and angle $COD$ is $\theta$ radians. Each of the sectors $BOA$ and $FOE$ has radius $r$, and $AOED$ and $CBOF$ are straight lines.