A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{13 π}{6}$ $(13 pi) / 6$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , 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 $\frac{13 π}{6}$ $(13 pi) / 6$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-07T09:59:17

$= 10.47$ $=10.47$

Explanation:

A chord that goes from $\frac{π}{2}$ $pi/2$ to $13 \frac{π}{6}$ $13pi/6$
so it travels the distance $13 \frac{π}{6} - \frac{π}{2} = 5 \frac{π}{3}$ $13pi/6-pi/2=5pi/3$ ;
or
$5 \frac{π}{3} \div 2 π = \frac{5}{6}$ $5pi/3-:2pi=5/6$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 4 π$ $=pir^2=4pi$
or
$r^{2} = 4$ $r^2=4$
or
$r = \sqrt{4}$ $r=sqrt4$
or
$r = 2$ $r=2$
Circumference of the circle $= 2 π r = 2 (π) (2) = 12.56$ $=2pir=2(pi)(2)=12.56$
Therefore Length of the chord $= 12.56 (\frac{5}{6}) = 10.47$ $=12.56(5/6)=10.47$

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{13 π}{6}$ $(13 pi) / 6$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , 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 $\frac{13 π}{6}$ $(13 pi) / 6$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?