A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{11 π}{6}$ $(11 pi) / 6$ radians on the circle. If the area of the circle is $5 π$ $5 pi$ , 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 $\frac{11 π}{6}$ $(11 pi) / 6$ radians on the circle. If the area of the circle is $5 π$ $5 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-08T10:01:04

$= 9.4$ $=9.4$

Explanation:

A chord that goes from $\frac{π}{2}$ $pi/2$ to $11 \frac{π}{6}$ $11pi/6$
so it travels the distance $11 \frac{π}{6} - \frac{π}{2} = 4 \frac{π}{3}$ $11pi/6-pi/2=4pi/3$ ;
or
$4 \frac{π}{3} \div 2 π = \frac{2}{3}$ $4pi/3-:2pi=2/3$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 5 π$ $=pir^2=5pi$
or
$r^{2} = 5$ $r^2=5$
or
$r = \sqrt{5}$ $r=sqrt5$
or
$r = 2.24$ $r=2.24$
Circumference of the circle $= 2 π r = 2 (π) (2.24) = 14.07$ $=2pir=2(pi)(2.24)=14.07$
Therefore Length of the chord $= 14.07 (\frac{2}{3}) = 9.4$ $=14.07(2/3)=9.4$

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{11 π}{6}$ $(11 pi) / 6$ radians on the circle. If the area of the circle is $5 π$ $5 pi$ , 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 $\frac{11 π}{6}$ $(11 pi) / 6$ radians on the circle. If the area of the circle is $5 π$ $5 pi$ , what is the length of the chord?