Question

Given that a circle has a radius $r$ and a sector that subtends an acute angle $\theta$ at the centre of the circle, then the perimeter of the sector is given by which of the following?

• A. $d(1+\frac{\theta \pi }{{180}^{\circ }})$
• B. $d(1+\frac{\theta \pi }{{360}^{\circ }})$
• C. $r(1+\frac{\theta \pi }{{360}^{\circ }})$
• D. $r(1+\frac{\theta \pi }{{180}^{\circ }})$

Answer 1

The correct option is B $d(1+\frac{\theta \pi }{{360}^{\circ }})$

Given that a circle has a radius $r$ and a sector that subtends an acute angle $\theta$ at the centre of the circle, then the perimeter of the sector is given by
$\text{arc length}+2r$
$=\frac{\theta }{{360}^{\circ }}\times 2\pi r+2r$
$=d(1+\frac{\theta \pi }{{360}^{\circ }})$