Question

A circle has a chord that goes from `( pi)/3` to `(4 pi) / 3` radians on the circle. If the area of the circle is `15 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=2sqrt15=7.75`

Explanation:

The angle subtended by the chord at the center of the circle is

`theta=4/3pi-1/3pi=3/3pi=pi`

The chord is the diameter of the circle

Let the radius of the circle be `=r`

The area of the circle is `A=pir^2`

Here, `A=15pi`

So,

`pir^2=15pi`

`r^2=15`

`r=sqrt15`

The length of the chord is

`l=2*sqrt15=7.75`