JAMB Mathematics 2016 Paper

Concept:The arc length of a circle is directly proportional to the angle it subtends at the centre.Explanation:Given arc length $L = 16\pi$ cm and central angle $\theta = 80^\circ$.Use the formula $L = \frac{\theta}{360^\circ} \times 2\pi r$.Substitute the given values: $16\pi = \frac{80}{360} \times 2\pi r$.Simplify the fraction: $\frac{80}{360} = \frac{2}{9}$.So $16\pi = \frac{2}{9} \times 2\pi r = \frac{4\pi r}{9}$.Cancel $\pi$ from both sides: $16 = \frac{4r}{9}$.Multiply both sides by 9: $144 = 4r$.Divide both sides by 4: $r = 36$.Answer:The radius of the circle is $36$ cm, which corresponds to option C.