JAMB Mathematics 2016 Paper

Concept:The perimeter of a sector is the total distance around it, which is the sum of the two radii and the arc length.Explanation:Use the formula for the perimeter of a sector:$$P = 2r + \frac{\theta}{360^\circ} \times 2\pi r$$Here, $r = 9\text{ cm}$ and $\theta = 36^\circ$.Substitute the values into the formula:$$P = 2(9) + \frac{36}{360} \times 2\pi(9)$$Simplify the fraction: $\frac{36}{360} = \frac{1}{10}$.Calculate the arc length:$$\frac{1}{10} \times 18\pi = \frac{18\pi}{10} = \frac{9\pi}{5}$$Add the two radii:$$P = 18 + \frac{9\pi}{5}$$Thus, the perimeter is $\left(18 + \frac{9\pi}{5}\right)\text{ cm}$.Answer:The correct answer is $\left(18 + \frac{9\pi}{5}\right)\text{ cm}$, which is option B.