Question

Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.

Answer 1

 

To find the length of an arc that subtends a central angle of 60° in a circle with a radius of 42 cm, we apply the formula for the arc length:

Arc length = `(θ​)/(360°)  xx 2πr`

 

Here, θ = 60° is the angle subtended by the arc at the centre, r = 42 cm is the radius of the circle, and π is approximately 3.14159.

Substituting the given values into the formula:

Arc length = `(60°)/(360°) xx 2 xx π xx 42  cm`

Arc length = `1/6 xx 2 xx π xx 42  cm`

Arc length= `1/3 xx 42  cm`

Arc length = `42/3 xx π  cm`

Arc length = 14 × π cm

Since π ≈ 3.14159, we have:

Arc length = 14 × 3.14159 cm

Arc length ≈ 43.98 cm

Therefore, the length of the arc is approximately 43.98 cm.