A circle has centre O and radius 12 cm . The sector AOB of the circle has area 126cm2 . Find the length of the arc AB.
Question
A circle has centre O and radius 12 cm . The sector AOB of the circle has area 126cm2 . Find the length of the arc AB.
Solution
Sure, here are the steps to find the length of the arc AB:
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First, we need to find the angle of the sector. The formula for the area of a sector is (θ/360) * π * r², where θ is the angle in degrees and r is the radius. We know the area is 126 cm² and the radius is 12 cm. So we can set up the equation:
126 = (θ/360) * π * 12²
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Solve for θ:
θ = (126 * 360) / (π * 12²) ≈ 75 degrees
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Now that we have the angle, we can find the length of the arc AB. The formula for the length of an arc is (θ/360) * 2πr. Substituting the values we have:
Length of arc AB = (75/360) * 2π * 12 ≈ 15.7 cm
So, the length of the arc AB is approximately 15.7 cm.
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