A circle has a chord that goes from ( 11 pi)/6 11π6 to (15 pi) / 8 15π8 radians on the circle. If the area of the circle is 128 pi 128π, what is the length of the chord?

1 Answer
Aug 9, 2016

=1.48=1.48

Explanation:

A chord that goes from (11pi)/611π6to (15pi)/815π8
so it travels the distance (15pi)/8-(11pi)/6=(pi)/2415π811π6=π24;
or
pi/24-:2pi=1/48π24÷2π=148 of the Circumference of the Circle
Area of the Circle=pir^2=128pi=πr2=128π
or
r^2=128r2=128
or
r=sqrt128r=128
or
r=11.3r=11.3
Circumference of the circle=2pir=2(pi)(11.3)=71=2πr=2(π)(11.3)=71
Therefore Length of the chord=71/48=1.48=7148=1.48