The areas of two sectors of two different cir | vedclass

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(B) No,it is not necessary that their corresponding arc lengths are equal.The area of a sector is given by $A = \frac{	heta}{360^\circ} 	imes \pi r^

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No

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(B) No,it is not necessary that their corresponding arc lengths are equal.The area of a sector is given by $A = \frac{	heta}{360^\circ} 	imes \pi r^2$,where $r$ is the radius and $	heta$ is the central angle.The arc length is given by $L = \frac{	heta}{360^\circ} 	imes 2\pi r$.From the area formula,we have $\frac{	heta}{360^\circ} = \frac{A}{\pi r^2}$.Substituting this into the arc length formula,we get $L = \frac{A}{\pi r^2} 	imes 2\pi r = \frac{2A}{r}$.Since the areas $A$ are equal,the arc length $L$ depends inversely on the radius $r$. If the radii of the two circles are different,the arc lengths will be different even if the areas of the sectors are equal.

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

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