The length of a minor arc in a circle with ra | vedclass

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Question

(A) Given: Radius $r = 28 \ cm$,Arc length $l = 22 \ cm$. $1$. To find the angle $	heta$ subtended at the centre: The formula for arc length is $l =

Vedclass · Accepted Answer

Angle: $45^{\circ}$,Area: $308 \ cm^2$

Vedclass · Answer

(A) Given: Radius $r = 28 \ cm$,Arc length $l = 22 \ cm$. $1$. To find the angle $	heta$ subtended at the centre: The formula for arc length is $l = \frac{	heta}{360^{\circ}} 	imes 2\pi r$. $22 = \frac{	heta}{360^{\circ}} 	imes 2 	imes \frac{22}{7} 	imes 28$. $22 = \frac{	heta}{360^{\circ}} 	imes 176$. $	heta = \frac{22 	imes 360^{\circ}}{176} = \frac{360^{\circ}}{8} = 45^{\circ}$. $2$. To find the area of the sector: The formula for the area of a sector is $A = \frac{	heta}{360^{\circ}} 	imes \pi r^2$. $A = \frac{45^{\circ}}{360^{\circ}} 	imes \frac{22}{7} 	imes 28 	imes 28$. $A = \frac{1}{8} 	imes 22 	imes 4 	imes 28 = 11 	imes 28 = 308 \ cm^2$.

The length of a minor arc in a circle with radius $28 \ cm$ is $22 \ cm$. Find the measure of the angle subtended at the centre by this arc. Also,find the area of the sector formed by this arc.

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