(a)[3]
Calculate the perimeter of sector $OAB$.
(b(i))[2]
Calculate the area of sector $OAB$.
(b(ii))[3]
Calculate the total shaded area.
(c)[4]
$D$ lies on the arc $AB$ such that $\angle AOD: \angle DOB = 1:2$. Gavin states that the shaded area in this diagram is the same as the shaded area found in part $b(ii)$. Is he correct? Show your working.