A circle has a chord that goes from ( pi)/3 to (15 pi) / 8 radians on the circle. If the area of the circle is 48 pi , what is the length of the chord?

1 Answer
Tony B
Jul 17, 2016

8sqrt(3)sin(37/48 pi) ~~9.14 to 2 decimal places

Explanation:

Area of a circle is pir^2
=> pir^2=48pi

=> r^2=48

=>r=sqrt(2^2xx2^2xx3)

=>r=4sqrt(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The angle of the arc is
(15pi)/8-pi/3" " =" " pi((45-8)/24)" "=" "37/24 pi

So 1/2 of this angle is 37/48pi

Tony B

The length of the chord is: 2(rsin(37/48 pi))

=8sqrt(3)sin(37/48 pi) ~~9.14 to 2 decimal places

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