In a circle of radius 22 cm, an arc subtends an angle of 45°at the centre. The l...

June 2021 2 27 Report

In a circle of radius 22 cm, an arc subtends an angle of 45°at the centre. The length of the arc
formed by the corresponding chord is?

$\blue{\huge{\underline{\underline{Answer:-}}}}$

Given :

In Circle, radius = 22 cm

angle subtended at centre is 45°

Length of arc = ?

$\\ length \: of \: arc \: = \frac{theta}{360} \times 2\pi \: r \\ \\ here \: theta \: is \: central \: angle$

$\\ \\ = \frac{45}{360} \times 2 \times 3.14 \times 22 \\ \\ = 0.125 \times 2 \times 3.14 \times 22 \\ \\ = 17.27 \: cm$

Therefore, length of arc formed is 17.27 cm

Length of the arc is always greater than length of corresponding chord
Length of the arc depends upon central angle as well as radius of the circle
Length of the arc decreases with central angle. Therefore, central angle(theta) is directly proportional to length of arc