Length of an arc formula

Let us consider a circle with radius r

Arc is a portion of the circle.

Let the arc subtend angle θ at the center

Then,

Angle at center = Length of Arc/ Radius of circle

θ = l/r

Note: Here angle is in radians.

Let’s take some examples

If radius of circle is 5 cm, and length of arc is 12 cm. Find angle subtended by arc

-a-

Given radius = r = 5 cm

Length of arc = l = 12 cm

We know that

  θ = l /r

  θ = 12/5

∴ Angle subtended by angle arc = 12/5 radians

-ea-

If angle subtended by arc is 1 radian, and radius of circle is 1 cm. Find length of arc

-a-

Given radius = r = 1 cm

Angle = θ = 1 radian

We know that

  θ = l /r

  1 = l /1

  1 = l

  l = 1 cm

∴ Length of the arc = 1 cm

-ea-

If angle subtended by arc is π radian, and length of the arc is 2 π cm. What is the radius of circle?

-a-

Given

Length of arc = l = 2π cm

Angle = θ = π radian

We know that

  θ = l /r

   π = 2π/r

  r = 2π/π

  r = 2 cm

∴ Radius of circle = 2 cm

-ea-