Question

A chord with a length of `6` runs from `pi/3` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

`412.53`

Explanation:

As the chord with a length of `6` runs from `pi/3` to `pi/2` radians, it is obvious that it subtends an angle of `pi/2-pi/3=pi/6`.

Hence, the chord subtends an angle of `pi/6` at center. Hence complete circumference, which subtends an angle of `2pi` should be of length

`6xx(2pi)/(pi/6)=6xx2pixx6/pi` i.e. `72`.

Hence, radius of circle is `72/(2pi)=36/pi`, and area of circle will be

`pixx(36/pi)^2=36xx36/pi=412.53`