question_answer

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If \[\angle AOB=~60{}^\circ \], find the area of the shaded region. [Use \[\pi =\frac{22}{7}\]]

Answer:

Angle for shaded region \[=360{}^\circ -60{}^\circ =300{}^\circ \]

Area of shaded region

\[=\frac{\pi \theta }{360}({{R}^{2}}-{{r}^{2}})\]

\[=\frac{22}{7}\times \frac{300}{360}[{{42}^{2}}-{{21}^{2}}]\]

\[=\frac{22}{7}\times \frac{5}{6}\times 63\times 21\]

= \[3465\,\,c{{m}^{2}}\]