Question

A circle has a chord that goes from `pi/4` to `pi/2` radians on the circle. If the area of the circle is `48 pi`, what is the length of the chord?

Answer 1

The length of a chord is `5.30` unit.

Explanation:

Formula for the length of a chord is `L_c= 2r sin (theta/2)`

where `r` is the radius of the circle and `theta` is the angle

subtended at the center by the chord. Area of circle is

`cancelpi * r^2 = 48 cancelpi :. r^2 = 48 or r = sqrt48 =4 sqrt3`

`theta= pi/2-pi/4 = pi/4 :. L_c= 2 *4sqrt3 *sin ((pi/4)/2)` or

`L_c= 2 * 4sqrt3 * sin (pi//8) = 8 sqrt3 * sin 22.5 [pi/8=22.5^0]` or

`L_c= 5.30` unit. The length of a chord is `5.30` unit.[Ans]