Question

Find the central angle of a sector of a circle having

(i) area $352c{m}^2$ and radius $12$ cm

(ii) area $462c{m}^2$ and radius $21$ cm

Answer 1

i)$\frac{\theta }{360°}\times \pi r^2=352c{m}^2\Rightarrow \frac{\theta }{360°}\times \frac{22}{7}\times {12}^2=352c{m}^2\Rightarrow \theta =\frac{352\times 360°\times 7}{22\times 14}=280°$

ii)$\frac{\theta }{360°}\times \pi r^2=462c{m}^2\Rightarrow \theta =\frac{462\times 360\times 7}{22\times 21\times 21}=120°$