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Question
Radius of a sector of a circle is 21 cm. If length of arc of that sector is 55 cm, find the area of the sector.
Solution
It is given that radius of circle = 21cm
length of arc of that sector is 55 cm
The ratio arc length of sector to circumference of circle is same as ratio of area of sector to area of circle
`"arc length"/ "circumference" = 55/(2πr)`
The area of sector is `55/(2πr)`of total area of circle with radius 21cm
To find area of circle with radius 21cm
Area = `πr^2`
To find the area of sector
Area of sector =`(55/(2pr)) xx πr^2 = (55r)/2 = (55 xx 21)/2 = 577.5 "cm"^2`
Therefore sector area = `577.5 "cm"^2`
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