A circle has a chord that goes from (2 pi)/3 to (7 pi) / 8 radians on the circle. If the area of the circle is 18 pi , what is the length of the chord?

1 Answer
Shwetank Mauria
Apr 18, 2016

Length of the chord is 2.73 units.

Explanation:

As the area of a circle is given by pir^2, where r is radius and area is given as 18pi

Radius is sqrt(18pi/pi)=sqrt18=3xxsqrt2

The angle covered by the chord is (7pi)/8-(2pi)/3=(21pi)/24-(16pi)/24=(5pi)/24

As length of chord is given by 2rsin(theta/2), where theta is angle covered by the chord.

Hence length of the chord is 2xx3xxsqrt2xxsin(5pi/48)

= 6xx1.4142xx0.32144=2.73

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