A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{7 π}{6}$ $(7 pi) / 6$ radians on the circle. If the area of the circle is $135 π$ $135 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{7 π}{6}$ $(7 pi) / 6$ radians on the circle. If the area of the circle is $135 π$ $135 pi$ , what is the length of the chord?

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Answer 1 · 2016-09-02T14:36:09

Length of the chord $= 36.5$ $=36.5$

Explanation:

A chord that goes from $\frac{π}{6}$ $(pi)/6$ to $\frac{7 π}{6}$ $(7pi)/6$
so it travels the distance $\frac{7 π}{6} - \frac{π}{6} = π$ $(7pi)/6-(pi)/6=pi$ ;
or
$π \div 2 π = \frac{1}{2}$ $pi-:2pi=1/2$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 135 π$ $=pir^2=135pi$
or
$r^{2} = 135$ $r^2=135$
or
$r = \sqrt{135}$ $r=sqrt135$
or
$r = 11.62$ $r=11.62$
Circumference of the circle $= 2 π r = 2 (π) (11.62) = 73$ $=2pir=2(pi)(11.62)=73$
Therefore Length of the chord $= 73 \times \frac{1}{2} = 36.5$ $=73times1/2=36.5$

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A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{7 π}{6}$ $(7 pi) / 6$ radians on the circle. If the area of the circle is $135 π$ $135 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from π6( pi)/6 to 7π6(7 pi) / 6 radians on the circle. If the area of the circle is 135π135 pi , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{7 π}{6}$ $(7 pi) / 6$ radians on the circle. If the area of the circle is $135 π$ $135 pi$ , what is the length of the chord?