A circle has a chord that goes from $\frac{5 π}{6}$ $( 5 pi)/6$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $18 π$ $18 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{5 π}{6}$ $( 5 pi)/6$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $18 π$ $18 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-23T11:34:41

Length of the chord $= 5.55$ $=5.55$

Explanation:

A chord that goes from $\frac{5 π}{6}$ $(5pi)/6$ to $\frac{5 π}{4}$ $(5pi)/4$
so it travels the distance $\frac{5 π}{4} - \frac{5 π}{6} = \frac{5 π}{12}$ $(5pi)/4-(5pi)/6=(5pi)/12$ ;
or
$\frac{5 π}{12} \div 2 π = \frac{5}{24}$ $(5pi)/12-:2pi=5/24$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 18 π$ $=pir^2=18pi$
or
$r^{2} = 18$ $r^2=18$
or
$r = \sqrt{18}$ $r=sqrt18$
or
$r = 4.24$ $r=4.24$
Circumference of the circle $= 2 π r = 2 (π) (4.24) = 26.66$ $=2pir=2(pi)(4.24)=26.66$
Therefore Length of the chord $= 26.66 \times \frac{5}{24} = 5.55$ $=26.66times5/24=5.55$

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A circle has a chord that goes from $\frac{5 π}{6}$ $( 5 pi)/6$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $18 π$ $18 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from ( 5 pi)/6 5π6( 5 pi)/6 to (5 pi) / 4 5π4(5 pi) / 4 radians on the circle. If the area of the circle is 18 pi 18π18 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{5 π}{6}$ $( 5 pi)/6$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $18 π$ $18 pi$ , what is the length of the chord?