Find the area of the sector of a circle of ra | vedclass

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Question

Let the central angle of the sector be $	heta$.

Given that, radius of the sector of a circle $( r )=5 \,cm$

and arc length $(l)=3.5\, cm$

$\

Vedclass · Accepted Answer

$8.75$

Vedclass · Answer

Let the central angle of the sector be $	heta$.

Given that, radius of the sector of a circle $( r )=5 \,cm$

and arc length $(l)=3.5\, cm$

$	herefore$ Central angle of the sector, $	heta=\frac{\operatorname{arc} 	ext { length }(l)}{	ext { radius }}$

$	heta=\frac{3.5}{5}=0.7 R \quad\left[\because 	heta=\frac{l}{r}ight]$

$	heta=\left(0.7 	imes \frac{180}{\pi}ight)^{\circ}\left[\because 1 R=\frac{180^{\circ}}{\pi} D^{\circ}ight]$

Now, area of sector with angle $	heta=0.7$

$=\frac{\pi r^{2}}{360^{\circ}} 	imes(0.7) 	imes \frac{180^{\circ}}{\pi}$

$=\frac{(5)^{2}}{2} 	imes 0.7=\frac{25 	imes 7}{2 	imes 10}=\frac{175}{20}=8.75 \,cm ^{2}$

Hence, required area of the sector of a circle is $8.75\, cm ^{2}$

Find the area of the sector of a circle of radius $5\, cm ,$ if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

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