Question

A circle has a chord that goes from `( 5 pi)/6` to `(5 pi) / 4` 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`=5.55`

Explanation:

A chord that goes from `(5pi)/6`to `(5pi)/4`
so it travels the distance `(5pi)/4-(5pi)/6=(5pi)/12`;
or
`(5pi)/12-:2pi=5/24` of the Circumference of the Circle
Area of the Circle`=pir^2=18pi`
or
`r^2=18`
or
`r=sqrt18`
or
`r=4.24`
Circumference of the circle`=2pir=2(pi)(4.24)=26.66`
Therefore Length of the chord`=26.66times5/24=5.55`