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प्रश्न
The area of a sector of a circle of 6 cm radius is 15 π sq. cm. Find the measure of the arc and the length of the arc corresponding to the sector.
The radius of a circle is 6 cm, the area of a sector of this circle is 15 π sq.cm. Find the measure of the arc and the length of the arc corresponding to that sector.
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उत्तर
Area of sector = `(l xx r)/2`
∴ `15 pi = (l xx 6)/2`
∴ `l = (15 x)/3`
∴ l = 5 π cm
∴ Length of the arc = 5 π cm.
Area of a sector = `theta/360 xx pi r^2`
∴ `15 pi = theta/360 xx pi xx 6^2`
∴ `15 = theta/360 xx 36`
∴ `15 = theta/10`
∴ θ = 150°
∴ Measure of the arc is 150°.
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