A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $144 π$ $144 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $144 π$ $144 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-28T13:31:57

$= 18.85$ $=18.85$

Explanation:

A chord that goes from $\frac{3 π}{4}$ $(3pi)/4$ to $\frac{5 π}{4}$ $(5pi)/4$
so it travels the distance $\frac{5 π}{4} - \frac{3 π}{4} = \frac{π}{2}$ $(5pi)/4-(3pi)/4=(pi)/2$ ;
or
$\frac{π}{2} \div 2 π = \frac{1}{4}$ $(pi)/2-:2pi=1/4$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 144 π$ $=pir^2=144pi$
or
$r^{2} = 144$ $r^2=144$
or
$r = \sqrt{144}$ $r=sqrt144$
or
$r = 12$ $r=12$
Circumference of the circle $= 2 π r = 2 (π) (12) = 75.4$ $=2pir=2(pi)(12)=75.4$
Therefore Length of the chord $= 75.4 \times \frac{1}{4} = 18.85$ $=75.4times1/4=18.85$

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $144 π$ $144 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from 3π4( 3 pi)/4 to 5π4(5 pi) / 4 radians on the circle. If the area of the circle is 144π144 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{5 π}{4}$ $(5 pi) / 4$ radians on the circle. If the area of the circle is $144 π$ $144 pi$ , what is the length of the chord?