Question

A chord with a length of `6` runs from `pi/8` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

Area `=91.6 unit^2`

Explanation:

The length of the chord is given by `l=2rsin(theta/2)`
`theta` is the angle at the center of the circle
where r is the radius of the circle and the area of the circle is `=pir^2`
`theta =pi/2-pi/8=(3pi)/8` and `theta/2=(3pi)/16`
`l=6=2rsin((3pi)/16)`
therefore, the radius `r=3/sin((3pi)/16)`
so the area of the circle is `pi*r^2=(9pi)/sin^2((3pi)/16)=91.6 u^2`