Question

How do you find the length of an arc of a circle with a radius of 12cm if the arc subtends a central angle of 30 degrees?

Answer 1

`color(blue)(l=6.28cm`

Explanation:

The formula for the length of an arc of a circle is:
`l=color(blue)(theta/360^o(2pir)`

Where:
`color(blue)(theta` is the angle subtended at the centre.
`color(blue)(2pir` is the circumference of the circle.

the circumference `2pir=(2 )* (3.14)*(12) = 75.36cm`

So, length of arc
`l=theta/(360^o) * (2pir)`

`l=30/(360^o) * (75.36)`

`l= (75.36)/12`

`color(blue)(l=6.28cm`