A circle has a chord that goes from $\frac{5 π}{4}$ $( 5 pi)/4$ to $\frac{4 π}{3}$ $(4 pi) / 3$ radians on the circle. If the area of the circle is $50 π$ $50 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{5 π}{4}$ $( 5 pi)/4$ to $\frac{4 π}{3}$ $(4 pi) / 3$ radians on the circle. If the area of the circle is $50 π$ $50 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-28T09:40:11

$= 1.85$ $=1.85$

Explanation:

A chord that goes from $\frac{5 π}{4}$ $(5pi)/4$ to $\frac{4 π}{3}$ $(4pi)/3$
so it travels the distance $\frac{4 π}{3} - \frac{5 π}{4} = \frac{π}{12}$ $(4pi)/3-(5pi)/4=(pi)/12$ ;
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 $= π r^{2} = 50 π$ $=pir^2=50pi$
or
$r^{2} = 50$ $r^2=50$
or
$r = \sqrt{50}$ $r=sqrt50$
or
$r = 7.1$ $r=7.1$
Circumference of the circle $= 2 π r = 2 (π) (7.1) = 44.43$ $=2pir=2(pi)(7.1)=44.43$
Therefore Length of the chord $= 44.43 \times \frac{1}{24} = 1.85$ $=44.43times1/24=1.85$

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A circle has a chord that goes from $\frac{5 π}{4}$ $( 5 pi)/4$ to $\frac{4 π}{3}$ $(4 pi) / 3$ radians on the circle. If the area of the circle is $50 π$ $50 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from 5π4( 5 pi)/4 to 4π3(4 pi) / 3 radians on the circle. If the area of the circle is 50π50 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 $\frac{5 π}{4}$ $( 5 pi)/4$ to $\frac{4 π}{3}$ $(4 pi) / 3$ radians on the circle. If the area of the circle is $50 π$ $50 pi$ , what is the length of the chord?