Question

A circle has a chord that goes from `( pi)/6` to `(7 pi) / 6` radians on the circle. If the area of the circle is `135 pi`, what is the length of the chord?

Answer 1

Length of the chord`=36.5`

Explanation:

A chord that goes from `(pi)/6`to `(7pi)/6`
so it travels the distance `(7pi)/6-(pi)/6=pi`;
or
`pi-:2pi=1/2` of the Circumference of the Circle
Area of the Circle`=pir^2=135pi`
or
`r^2=135`
or
`r=sqrt135`
or
`r=11.62`
Circumference of the circle`=2pir=2(pi)(11.62)=73`
Therefore Length of the chord`=73times1/2=36.5`