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

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

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Answer 1 · 2016-08-28T13:36:31

$= 1.18$ $=1.18$

Explanation:

A chord that goes from $\frac{π}{3}$ $(pi)/3$ to $\frac{3 π}{8}$ $(3pi)/8$
so it travels the distance $\frac{3 π}{8} - \frac{π}{3} = \frac{π}{24}$ $(3pi)/8-(pi)/3=(pi)/24$ ;
or
$\frac{π}{24} \div 2 π = \frac{1}{48}$ $(pi)/24-:2pi=1/48$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 81 π$ $=pir^2=81pi$
or
$r^{2} = 81$ $r^2=81$
or
$r = \sqrt{81}$ $r=sqrt81$
or
$r = 9$ $r=9$
Circumference of the circle $= 2 π r = 2 (π) (9) = 56.55$ $=2pir=2(pi)(9)=56.55$
Therefore Length of the chord $= 56.55 \times \frac{1}{48} = 1.18$ $=56.55times1/48=1.18$

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

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