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  • Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector

Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

Answers (1)

\left [ 73\frac{1}{3}cm \right ] 

Solution

Area of sector=\frac{\pi r^{2}\theta}{360}

Angle = 200°

  Area of sector = 770 cm2    

\\\frac{\pi r^{2}\theta}{360}=770\\\\ \pi r^{2} \times 200^{\circ}=770 \times 360 ^{\circ}\\\\ r^{2}=\frac{770 \times 360 ^{\circ} \times 7}{200^{\circ \times 22}} \;\;\; \left [ here \pi=\frac{22}{7} \right ]\\\\ r^{2}=49 \times 9\\ r=\sqrt{49 \times 9}=7 \times 3=21cm

Length of the corresponding arc =\frac{\theta \times 2\pi r}{360}
\\=\frac{200^{\circ} \times 2 \times \pi \times 21}{360^{\circ}}\\\\ =\frac{10 \times 7}{3}\times\frac{22}{7}\\\\ =\frac{220}{3}\\\\ =73\frac{1}{3}cm

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infoexpert24

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