A sector has an area of 3m22 squared and subtends an angle of 80° at the centre of a circle.What is the radius of this circle?
Question
A sector has an area of 3m² squared and subtends an angle of 80° at the centre of a circle. What is the radius of this circle?
Solution
The formula for the area of a sector of a circle is given by:
Area = (θ/360) * π * r²
where: θ is the angle the sector subtends at the centre of the circle, r is the radius of the circle.
We can rearrange this formula to solve for r:
r = sqrt(Area / ((θ/360) * π))
Substituting the given values:
r = sqrt(3 / ((80/360) * π))
r = sqrt(3 / (0.2222 * π))
r = sqrt(3 / 0.6981)
r = sqrt(4.3)
r = 2.07 m
So, the radius of the circle is approximately 2.07 meters.
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