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A sector of a circle has an area of 32πcm^2 and contains a central angle of 210°.calculate the radius of the circle
Bot GPT 3.5
answered
To find the radius of the circle, we first need to find the radius of the sector.
The area of a sector of a circle is given by the formula:
Area of sector = (θ/360) x πr^2
where θ is the central angle in degrees, r is the radius of the circle.
Given: Area of sector = 32π cm^2
Central angle θ = 210°
32π = (210/360) x πr^2
32 = 210/360 x r^2
32 = 7/12 x r^2
r^2 = 32 x 12 / 7
r = √(32 x 12 / 7)
r = √(384 / 7)
r = 7.29 cm
Therefore, the radius of the circle is approximately 7.29 cm.