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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