Find the difference of the areas of a sector | vedclass

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Question

(C) Given that,the radius of the circle $(r) = 21 \, cm$ and the central angle of the minor sector $(	heta) = 120^{\circ}$.First,calculate the total

Vedclass · Accepted Answer

$462$

Vedclass · Answer

(C) Given that,the radius of the circle $(r) = 21 \, cm$ and the central angle of the minor sector $(	heta) = 120^{\circ}$.First,calculate the total area of the circle:Area $= \pi r^2 = \frac{22}{7} 	imes (21)^2 = \frac{22}{7} 	imes 21 	imes 21 = 22 	imes 3 	imes 21 = 1386 \, cm^2$.Next,calculate the area of the minor sector:Area of minor sector $= \frac{	heta}{360^{\circ}} 	imes \pi r^2 = \frac{120^{\circ}}{360^{\circ}} 	imes 1386 = \frac{1}{3} 	imes 1386 = 462 \, cm^2$.Then,calculate the area of the major sector:Area of major sector $= 	ext{Total area} - 	ext{Area of minor sector} = 1386 - 462 = 924 \, cm^2$.Finally,find the difference between the areas of the major sector and the minor sector:Difference $= 924 - 462 = 462 \, cm^2$.

Find the difference of the areas of a sector of angle $120^{\circ}$ and its corresponding major sector of a circle of radius $21 \, cm$. (in $cm^2$)

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