Question

A circle has a chord that goes from `( 3 pi)/4` to `(15 pi) / 8` radians on the circle. If the area of the circle is `54 pi`, what is the length of the chord?

Answer 1

`=26`

Explanation:

A chord that goes from `(3pi)/4`to `(15pi)/8`
so it travels the distance `(15pi)/8-(3pi)/4=(9pi)/8`;
or
`(9pi)/8-:2pi=9/16` of the Circumference of the Circle
Area of the Circle`=pir^2=54pi`
or
`r^2=54`
or
`r=sqrt54`
or
`r=7.35`
Circumference of the circle`=2pir=2(pi)(7.35)=46.17`
Therefore Length of the chord`=46.17times9/16=26`