MATHEMATICS

JAMB 2016 - Question 31

Mathematics 2016 JAMB Past Questions - Question 31: An arc of the length 16πcm substends an angle of 80 at the centre of the circle. find the circle.

An arc of the length 16πcm substends an angle of 80 at the centre of the circle. find the circle.
A:
B:
C:
D:
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Correct Answer

C

Explanation

length of arc = 80 / 360 - 2πri.e. 16π = 80 / 369 x 2πr16π x 36 = 80 x 2πtherefore r = 16π x 360 /80 x 2π36cmTo find the radius of the circle, we can use the formula relating the arc length, angle, and radius of a circle:Arc Length = Radius × Angle in RadiansIn this case, the arc length is 16π cm and the angle is 80 degrees. We need to convert the angle from degrees to radians because the formula uses radians.1 degree = π/180 radiansSo, 80 degrees = 80 × π/180 radians = 4π/9 radiansNow we can use the formula:16π = Radius × (4π/9)Solving for the radius:Radius = (16π) / (4π/9)      = (16π) × (9/4π)      = 36 cmTherefore, the radius of the circle is 36 cm.