Question

A circle has a chord that goes from `( 3 pi)/8` to `(5 pi) / 3` radians on the circle. If the area of the circle is `36 pi`, what is the length of the chord?

Answer 1

Length of the chord`=24.35`

Explanation:

A chord that goes from `(3pi)/8`to `(5pi)/3`
so it travels the distance `(5pi)/3-(3pi)/8=(31pi)/24`;
or
`(31pi)/24-:2pi=31/48` of the Circumference of the Circle
Area of the Circle`=pir^2=36pi`
or
`r^2=36`
or
`r=sqrt36`
or
`r=6`
Circumference of the circle`=2pir=2(pi)(6)=37.7`
Therefore Length of the chord`=37.7times31/48=24.35`