A circle has a chord that goes from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on the circle. If the area of the circle is $25 π$ $25 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on the circle. If the area of the circle is $25 π$ $25 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-07T09:25:28

$= 0.65$ $=0.65$

Explanation:

A chord that goes from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$
so it travels the distance $\frac{π}{8} - \frac{π}{12} = \frac{π}{24}$ $pi/8-pi/12=pi/24$ ;
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 $= π r^{2} = 25 π$ $=pir^2=25pi$
or
$r^{2} = 25$ $r^2=25$
or
$r = \sqrt{25}$ $r=sqrt25$
or
$r = 5$ $r=5$
Circumference of the circle $= 2 π r = 2 (π) (5) = 31.41$ $=2pir=2(pi)(5)=31.41$
Therefore Length of the chord $= \frac{31.41}{48} = 0.65$ $=31.41/48=0.65$

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A circle has a chord that goes from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on the circle. If the area of the circle is $25 π$ $25 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on the circle. If the area of the circle is $25 π$ $25 pi$ , what is the length of the chord?