Mathematics 2019 JAMB Past Questions - Question 18: Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 450

Correct Answer

C

Explanation

To calculate the perimeter of a sector of a circle, you need to find the arc length and add it to twice the radius.First, let's find the arc length of the sector. The formula for the arc length of a sector of a circle is given by \( \frac{n}{360} \times 2\pi r \), where \( n \) is the angle in degrees and \( r \) is the radius.In this case, the angle is 45 degrees and the radius is 8 cm. Plugging these values into the formula gives:Arc length = \( \frac{45}{360} \times 2\pi \times 8 \)Arc length = \( \frac{1}{8} \times 16\pi \)Arc length = 2π cmNow, the perimeter of the sector is the sum of the arc length and twice the radius:Perimeter = 2π + 2(8)Perimeter = 2π + 16So, the perimeter of the sector is \( 2π + 16 \) cm.