Question

A circle has a chord that goes from `( 3 pi)/4` to `(5 pi) / 4` radians on the circle. If the area of the circle is `144 pi`, what is the length of the chord?

Answer 1

`=18.85`

Explanation:

A chord that goes from `(3pi)/4`to `(5pi)/4`
so it travels the distance `(5pi)/4-(3pi)/4=(pi)/2`;
or
`(pi)/2-:2pi=1/4` of the Circumference of the Circle
Area of the Circle`=pir^2=144pi`
or
`r^2=144`
or
`r=sqrt144`
or
`r=12`
Circumference of the circle`=2pir=2(pi)(12)=75.4`
Therefore Length of the chord`=75.4times1/4=18.85`