Question

In given fig. of sector of circle of radius 10.5 cm. What is the perimeter of sector?

Answer 1

Perimeter of the sector $=AC$$+$$BC$$+$arc $AB$

$AC=BC=radius=10.5$ cm

Length of the arc of the sector with central angle, $\theta$ (in degree) is $=\frac{\theta }{360}\times 2\pi r$

So, length of the arc AB$=\frac{60}{360}\times 2\pi \times \left(10.5\right)$

$=\frac{1}{3}\times \frac{22}{7}\times \left(10.5\right)$

$=11$ cm

Perimeter of the sector $=10.5+10.5+11=32$ cm