A circle has a chord that goes from $\frac{4 π}{3}$ $( 4 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{4 π}{3}$ $( 4 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-13T14:43:09

$= 1.36$ $=1.36$

Explanation:

A chord that goes from $\frac{4 π}{3}$ $(4pi)/3$ to $\frac{17 π}{12}$ $(17pi)/12$
so it travels the distance $\frac{17 π}{12} - \frac{4 π}{3} = \frac{π}{12}$ $(17pi)/12-(4pi)/3=(pi)/12$ ;
or
$\frac{π}{12} \div 2 π = \frac{1}{24}$ $(pi)/12-:2pi=1/24$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 27 π$ $=pir^2=27pi$
or
$r^{2} = 27$ $r^2=27$
or
$r = \sqrt{27}$ $r=sqrt27$
or
$r = 5.2$ $r=5.2$
Circumference of the circle $= 2 π r = 2 (π) (5.2) = 32.67$ $=2pir=2(pi)(5.2)=32.67$
Therefore Length of the chord $= 32.67 \times \frac{1}{24} = 1.36$ $=32.67times1/24=1.36$

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A circle has a chord that goes from $\frac{4 π}{3}$ $( 4 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from 4π3( 4 pi)/3 to 17π12(17 pi) / 12 radians on the circle. If the area of the circle is 27π27 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 $\frac{4 π}{3}$ $( 4 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?