A) 4cm
B) 8cm
C) 12cm
D) 16cm
Correct Answer: B
Solution :
Let the radius of the circle be r cm and the arc AB of length \[5\pi \]cm subtends angle \[\theta \] at the centre O of the circle. Then, arc \[AB=5\pi \] cm and area of the sector \[OAB=20\pi \,c{{m}^{2}}\] \[\Rightarrow \,\,\frac{\theta }{360{}^\circ }\times 2\pi r=5\pi \] And \[\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}=20\pi \] \[\Rightarrow \,\,\frac{\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}}{\frac{\theta }{360{}^\circ }\times 2\pi r}=\frac{20\pi }{5\pi }\] \[\Rightarrow \frac{r}{2}=4\,\,\Rightarrow r=8\,cm\]You need to login to perform this action.
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