In a circle with radius 56 , cm,find the area | vedclass

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Question

(A) Given radius $r = 56 \, cm$. Since the two radii are perpendicular,the central angle $	heta = 90^\circ$.Area of the minor sector = $\frac{	heta}

Vedclass · Accepted Answer

Minor sector: $2464 \, cm^2$,Major sector: $7392 \, cm^2$,Minor segment: $896 \, cm^2$

Vedclass · Answer

(A) Given radius $r = 56 \, cm$. Since the two radii are perpendicular,the central angle $	heta = 90^\circ$.Area of the minor sector = $\frac{	heta}{360^\circ} 	imes \pi r^2 = \frac{90}{360} 	imes \frac{22}{7} 	imes 56 	imes 56 = \frac{1}{4} 	imes 22 	imes 8 	imes 56 = 2464 \, cm^2$.Area of the major sector = Total area of circle - Area of minor sector = $\pi r^2 - 2464 = \frac{22}{7} 	imes 56 	imes 56 - 2464 = 9856 - 2464 = 7392 \, cm^2$.Area of the minor segment = Area of minor sector - Area of triangle = $2464 - \frac{1}{2} 	imes r^2 	imes \sin(90^\circ) = 2464 - \frac{1}{2} 	imes 56 	imes 56 	imes 1 = 2464 - 1568 = 896 \, cm^2$.

In a circle with radius $56 \, cm$,find the area of the minor sector,the major sector,and the minor segment corresponding to two radii perpendicular to each other.

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