Question

the area of a sector of a circle of radius 10 cm is 75 cm square . find the length of corresponding arc of the circle


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Answer 1

Step-by-step explanation:

Let α be the angle of the sector.

Area of sector =

$\frac{ \alpha }{360} \times \pi {r}^{2}$

And length of arc, l = α×r

α = l / r

$75 = \frac{ \alpha }{360} \times \ (\frac{22}{7} )( {10})^{2} \\ \\ 75 = \frac{ \frac{l}{r} }{360} \times ( \frac{22}{7} )(100) \\ 75 = \frac{l}{10 \times 360} \times \frac{22}{7 } \times 100 \\ 75 = \frac{l}{36} \times \frac{22}{7} \\ l = \frac{75 \times 36 \times 7}{22} = 859.09 \: cm$