JAMB 1990 · UME · Q32

The angle of a sector of a circle of radius 10.5 cm is $48^\circ$ . Calculate the perimeter of the sector. $\left[\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Arc length $= \frac{\theta}{360} \times 2\pi r$ .
The circumference is $2 \times \frac{22}{7} \times 10.5 = 66$ cm, so the arc is $\frac{48}{360} \times 66 = 8.8$ cm.
The perimeter adds the two radii: $8.8 + 2 \times 10.5 = 29.8$ cm, option D.