A circle has a chord that goes from $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{11 π}{12}$ $(11 pi) / 12$ 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 $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{11 π}{12}$ $(11 pi) / 12$ 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 · 2016-08-16T16:14:53

Length of the chord $= 1.76$ $=1.76$

Explanation:

A chord that goes from $\frac{2 π}{3}$ $(2pi)/3$ to $\frac{11 π}{12}$ $(11pi)/12$
so it travels the distance $\frac{11 π}{12} - \frac{2 π}{3} = \frac{π}{4}$ $(11pi)/12-(2pi)/3=(pi)/4$ ;
or
$\frac{π}{4} \div 2 π = \frac{1}{8}$ $(pi)/4-:2pi=1/8$ 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 $= 2 π r = 2 (π) (2.24) = 14.05$ $=2pir=2(pi)(2.24)=14.05$
Therefore Length of the chord $= 14.05 \times \frac{1}{8} = 1.76$ $=14.05times1/8=1.76$

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A circle has a chord that goes from $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{11 π}{12}$ $(11 pi) / 12$ 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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Explanation:

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A circle has a chord that goes from 2π3( 2 pi)/3 to 11π12(11 pi) / 12 radians on the circle. If the area of the circle is 5π5 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{11 π}{12}$ $(11 pi) / 12$ radians on the circle. If the area of the circle is $5 π$ $5 pi$ , what is the length of the chord?