Question

What is the perimeter of a sector whose end points subtend a ${45}^{\circ }$ angle at the center of a circle of radius $8$ inches?

• A. $14+2\pi$ inches
• B. $14+4\pi$ inches
• C. $16+2\pi$ inches
• D. $16+4\pi$ inches

Answer 1

The correct option is C $16+2\pi$ inches

Perimeter of a sector $=\frac{\theta }{{360}^{\circ }}\times 2\pi r+2r$
Perimeter $=\frac{{45}^{\circ }}{{360}^{\circ }}\times 2\pi \left(8\right)+2\left(8\right)$
Perimeter = $2\pi +16$ inches