Calculate the length of the arc of a circle if: i. the radius is 3.5 cm and the angle at the centre is 60°

Calculate the length of the arc of a circle if: i. the radius is 3.5 cm and the angle at the centre is 60°

Question 1.

Calculate the length of the arc of a circle if: Class 9

i. the radius is 3.5 cm and the angle at the centre is 60°, and

ii. the radius is 6.3 m and the angle at the centre is 120°.

Solution:

i. Given:

Radius (r) = 3.5 cm, Angle (θ) = 60°

∴ Length of arc

$\begin{aligned} & =\frac{\theta}{360^{\circ}} \times 2 \pi r \\ & =\frac{60}{360} \times 2 \times \frac{22}{7} \times 3.5 \\ & =\frac{1}{6} \times 2 \times \frac{22}{7} \times 3.5 \\ & =\frac{1}{6} \times 22 \\ & =\frac{22}{6} \mathrm{~cm}\end{aligned}$

= 3.67 cm

∴ The length of the arc is 3.67 cm.

ii. Radius (r) = 6.3 m, Angle (θ) = 120°

∴ Length of arc

$\begin{aligned} & =\frac{\theta}{360^{\circ}} \times 2 \pi r \\ & =\frac{120}{360} \times 2 \times \frac{22}{7} \times 6.3 \\ & =\frac{1}{3} \times 2 \times \frac{22}{7} \times 6.3\end{aligned}$

$\begin{aligned} & =\frac{1}{3} \times \frac{44}{7} \times 6.3 \\ & =\frac{1}{3} \times 44 \times 0.9 \\ & =\frac{39.6}{3}\end{aligned}$

= 13.2 m

∴ The length of the arc is 13.2 m.