Question

Find the length of the arc in terms of pi

Answer 1

`(\beta )/(2\pi ) *2\pi r\\`

Explanation:

We know that perimeter of a circle is given by 2πr (where r is the radius of the circle).

We can say that for an complete angle of 2π the perimeter is 2πr.

Now let us consider a small section of segment making an angle β at the centre.

According to the proportionality rules the length of the small segment would be

`(\beta )/(2\pi ) *2\pi r\\`

Let the perimeter of circle be P then

`(\beta )/(2\pi ) *P`

Hence this is the formula for length of an arc subtending angle β.