In a circle with radius 14 ,cm,an arc subtend | vedclass

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Question

(A) Given: Radius $r = 14 \,cm$,Angle $	heta = 90^\circ$.$1$. Length of arc = $\frac{	heta}{360^\circ} 	imes 2\pi r = \frac{90}{360} 	imes 2 	ime

Vedclass · Accepted Answer

Length of arc: $22 \,cm$,Area of sector: $154 \,cm^2$,Area of segment: $56 \,cm^2$

Vedclass · Answer

(A) Given: Radius $r = 14 \,cm$,Angle $	heta = 90^\circ$.$1$. Length of arc = $\frac{	heta}{360^\circ} 	imes 2\pi r = \frac{90}{360} 	imes 2 	imes \frac{22}{7} 	imes 14 = \frac{1}{4} 	imes 88 = 22 \,cm$.$2$. Area of minor sector = $\frac{	heta}{360^\circ} 	imes \pi r^2 = \frac{90}{360} 	imes \frac{22}{7} 	imes 14 	imes 14 = \frac{1}{4} 	imes 22 	imes 28 = 154 \,cm^2$.$3$. Area of minor segment = Area of sector - Area of triangle = $154 - \frac{1}{2} 	imes r^2 	imes \sin(90^\circ) = 154 - \frac{1}{2} 	imes 14 	imes 14 	imes 1 = 154 - 98 = 56 \,cm^2$.

In a circle with radius $14 \,cm$,an arc subtends a right angle at the centre. Find the length of this arc,the area of the minor sector,and the area of the minor segment formed by it.

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