Question

A chord with a length of `4` runs from `pi/4` to `pi/3` radians on a circle. What is the area of the circle?

Answer 1

`733.386`

Explanation:

As the chord with a length of `4` runs from `pi/4` to `pi/3` radians, it is obvious that it subtends an angle of `pi/3-pi/4=pi/12`.

Hence complete circumference, which subtends an angle of `2pi` should be of length

`4xx(2pi)/(pi/12)=4xx2pixx12/pi` i.e. `96`.

Hence, radius of circle is `96/(2pi)=48/pi`, and area of circle will be

`pixx(48/pi)^2=48xx48/pi=733.386`