question_answer

In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where\[\angle AOC=40{}^\circ \]. (Use \[\pi =\frac{22}{7}\])

Answer:

Given, \[r=7\text{ }cm\] and \[R=14\text{ }cm\] .

Area of shaded region \[=\pi ({{R}^{2}}-{{r}^{2}})\frac{\theta }{360{}^\circ }\]

\[=\frac{22}{7}({{14}^{2}}-{{7}^{2}})\times \frac{(360{}^\circ -40{}^\circ )}{360{}^\circ }\]

\[=\frac{22}{7}\times 7\times 21\times \frac{320{}^\circ }{360{}^\circ }\]

\[=410.67\,\,c{{m}^{2}}\]