Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle Class 9

Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle Class 9

Question 1.

Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle of radius 14 cm and sector angle 75°. Class 9

Solution:

Radius (r) = 14cm, Angle (θ) = 75°

Length of arc

$\begin{aligned} & =\frac{\theta}{360^{\circ}} \times 2 \pi r \\ & =\frac{75}{360} \times 2 \times \frac{22}{7} \times 14 \\ & =\frac{75}{360} \times 88 \\ & =\frac{5}{24} \times 88 \\ & =\frac{440}{24}\end{aligned}$

∴ Length of arc = 18.33 cm

Perimeter of Sector = Length of arc + 2r

∴ = 18.33 + 28

∴ = 46.33 cm

The perimeter of the sector is 46.33 cm.