Question

$AB$ and $CD$ are respectively arc of two concentric circles of radius $21cm$ and $7cm$ and center $O$. If $\angle AOB={30}^o$, find the area of the OCD,OAB.

Answer 1

As shaded region is missing, finding both $OCD$ and $OAB$ areas,

Area of a sector $=\frac{1}{2}{r}^2\sin 0$

$\Rightarrow$ Area of $OCD=\frac{1}{2}(7{)}^2\sin 30=\frac{49}{2}\times \frac{1}{2}=\frac{49}{4}cm$

Area of $OAB=\frac{1}{2}(21{)}^2\sin 30=\frac{441}{4}c{m}^2$.