Question

A circle has a chord that goes from `(2 pi)/3` to `(7 pi) / 8` radians on the circle. If the area of the circle is `18 pi`, what is the length of the chord?

Answer 1

Length of the chord is `2.73` units.

Explanation:

As the area of a circle is given by `pir^2`, where `r` is radius and area is given as `18pi`

Radius is `sqrt(18pi/pi)=sqrt18=3xxsqrt2`

The angle covered by the chord is `(7pi)/8-(2pi)/3=(21pi)/24-(16pi)/24=(5pi)/24`

As length of chord is given by `2rsin(theta/2)`, where `theta` is angle covered by the chord.

Hence length of the chord is `2xx3xxsqrt2xxsin(5pi/48)`

= `6xx1.4142xx0.32144=2.73`