A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{15 π}{8}$ $(15 pi) / 8$ radians on the circle. If the area of the circle is $42 π$ $42 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{15 π}{8}$ $(15 pi) / 8$ radians on the circle. If the area of the circle is $42 π$ $42 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-06T10:06:55

$= 28$ $=28$

Explanation:

A chord that goes from $\frac{π}{2}$ $pi/2$ to $15 \frac{π}{8}$ $15pi/8$
so it travels the distance $15 \frac{π}{8} - \frac{π}{2} = 11 \frac{π}{8}$ $15pi/8-pi/2=11pi/8$ ;
or
$11 \frac{π}{8} \div 2 π = \frac{11}{16}$ $11pi/8-:2pi=11/16$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 12 π$ $=pir^2=12pi$
or
$r^{2} = 42$ $r^2=42$
or
$r = \sqrt{42}$ $r=sqrt42$
or
$r = 6.48$ $r=6.48$
Circumference of the circle $= 2 π r = 2 (π) (6.48) = 40.72$ $=2pir=2(pi)(6.48)=40.72$
Therefore Length of the chord $= 40.72 (\frac{11}{16}) = 28$ $=40.72(11/16)=28$

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{15 π}{8}$ $(15 pi) / 8$ radians on the circle. If the area of the circle is $42 π$ $42 pi$ , what is the length of the chord?

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A circle has a chord that goes from ( pi)/2 π2( pi)/2 to (15 pi) / 8 15π8(15 pi) / 8 radians on the circle. If the area of the circle is 42 pi 42π42 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{15 π}{8}$ $(15 pi) / 8$ radians on the circle. If the area of the circle is $42 π$ $42 pi$ , what is the length of the chord?