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प्रश्न
The area of a circle is 81π sq.cm. Find the length of the arc subtending an angle of 300° at the centre and also the area of corresponding sector.
उत्तर
Let 'r' be the radius of a circle whose area is 225 π sq. cm.
Area of circle = πr2
But area is given to be 81π sq. cm.
∴ πr2 = 81π
∴ r2 = 81
∴ r = 9 cm
θ = 300°
= `(300 xx pi/180)^c`
= `((5pi)/3)^c`
Since S = r × θ,
S = `9 xx (5pi)/3`
∴ S = 15 π cm
Area of sector = `1/2r^2theta`
= `1/2 xx 9 xx 9 xx (5pi)/3`
= `1/2 xx 9 xx cancel(9)^3 xx (5pi)/cancel(3)_1`
= `(135 pi)/2` sq. cm
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