Arc Length Formula

Arc Length Formula is used to find thelength of an arc of a circle. Arc Length of a Circle is defined as the length of the arc formed byan angle θ in a circle of radius r. The arc length of a circle is given by the arc length formula,

S = r.θ, Where S represents the arc length, r represents the radius ofthe circle and θ represents the angle in radians made by the arc at the centre of the circle.

In the above figure, arc length of the circle formed by an angle θ is shown in red colour on the circumference of the circle.

Here are few solved problems applying the length of arc formula:

Problem 1

Find the arc length of the arc, if θ = 60⁰ and r = 21

Solution

The formula for arc length is as follows,

Length of arc = 2πr θ/360⁰

Putting the values of angle θ⁰ and the radius in the formula we get

= 2 × 22/7 × 21 × 60⁰/360⁰

By solving this we get,

= 22 cm

Problem 2

Find the angle subtended by an arc of length 44 and radius by applying the formula

Solution

Arc Length of a Circle Formula is as follows,

Length of arc = 2πr θ/360⁰

Putting the values of length of arc and radius in the formula we get,

44 = 2πr θ/360⁰

θ = 44 × 360 × 7/2 × 22 × 28

= 90⁰

So arc subtends 90⁰ angle of centre

Problem 3

In the given figure, if the length of arc is given as 11 cm and radius of the circle is 21 cm, find the angle Q of the arc.

Solution

We get the length of the arc by using the formula,

Length of arc = 2 π r ×Q⁰/360⁰

According to the problem, we have to find angle Q⁰

Length of arc × 360⁰/ 2 π r

Putting the values of length of arc and radius in the above formula, we get,

Q⁰ = 11 × 360⁰/2.π.21

By solving this, we get the angle Q⁰ = 30⁰