Question

A circle has a chord that goes from `( pi)/8` to `(5 pi) / 6` radians on the circle. If the area of the circle is `225 pi`, what is the length of the chord?

Answer 1

`=33.38`

Explanation:

A chord that goes from `(pi)/8`to `(5pi)/6`
so it travels the distance `(5pi)/6-(pi)/8=(17pi)/24`;
or
`(17pi)/24-:2pi=17/48` of the Circumference of the Circle
Area of the Circle`=pir^2=225pi`
or
`r^2=225`
or
`r=sqrt225`
or
`r=15`
Circumference of the circle`=2pir=2(pi)(15)=94.24`
Therefore Length of the chord`=94.24times17/48=33.38`