A circle has a chord that goes from pi/4 to (3 pi) / 8 radians on the circle. If the area of the circle is 81 pi , what is the length of the chord?

1 Answer
Binayaka C.
Nov 17, 2017

The length of the chord is 3.51 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 = 81 cancelpi :. r^2 = 81 or r = sqrt81 =9.0

theta= (3pi)/8-pi/4 = pi/8 :. L_c= 2 *9 *sin ((pi/8)/2) or

L_c= 18 * sin (pi/16) ~~ 3.51 (2dp) orL_c ~~ 3.51 (2dp) unit.

The length of the chord is 3.51 unit.[Ans]

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