Area of a sector of central angle 200^{circ} | vedclass

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Question

(B) Let the radius of the circle be $r$ and the central angle be $	heta = 200^{\circ}$.Area of the sector is given by the formula: $	ext{Area} = \fr

Vedclass · Accepted Answer

$73 \frac{1}{3}$

Vedclass · Answer

(B) Let the radius of the circle be $r$ and the central angle be $	heta = 200^{\circ}$.Area of the sector is given by the formula: $	ext{Area} = \frac{	heta}{360^{\circ}} 	imes \pi r^{2}$.Substituting the given values: $770 = \frac{200}{360} 	imes \frac{22}{7} 	imes r^{2}$.$770 = \frac{5}{9} 	imes \frac{22}{7} 	imes r^{2}$.$r^{2} = \frac{770 	imes 9 	imes 7}{5 	imes 22} = \frac{770 	imes 63}{110} = 7 	imes 63 = 441$.$r = \sqrt{441} = 21 \, cm$.Now,the length of the arc $l$ is given by: $l = \frac{	heta}{360^{\circ}} 	imes 2\pi r$.$l = \frac{200}{360} 	imes 2 	imes \frac{22}{7} 	imes 21$.$l = \frac{5}{9} 	imes 2 	imes 22 	imes 3 = \frac{5 	imes 2 	imes 22}{3} = \frac{220}{3} \, cm$.$l = 73 \frac{1}{3} \, cm$.

Area of a sector of central angle $200^{\circ}$ of a circle is $770 \, cm^{2}$. Find the length of the corresponding arc of this sector. (in $cm$)

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