Question

A circle has a chord that goes from `( pi)/3` to `(15 pi) / 8` radians on the circle. If the area of the circle is `48 pi`, what is the length of the chord?

Answer 1

`8sqrt(3)sin(37/48 pi) ~~9.14` to 2 decimal places

Explanation:

Area of a circle is `pir^2`
`=> pir^2=48pi`

`=> r^2=48`

`=>r=sqrt(2^2xx2^2xx3)`

`=>r=4sqrt(3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The angle of the arc is
`(15pi)/8-pi/3" " =" " pi((45-8)/24)" "=" "37/24 pi`

So 1/2 of this angle is `37/48pi`

The length of the chord is: `2(rsin(37/48 pi))`

`=8sqrt(3)sin(37/48 pi) ~~9.14` to 2 decimal places