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 $42 π$ $42 pi$ , 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 $42 π$ $42 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-04T23:15:49

$= 1.7$ $=1.7$

Explanation:

Area of the circle $= π r^{2} = 42 π$ $=pir^2=42pi$
or
$r^{2} = 42$ $r^2=42$
or
$r = \sqrt{42}$ $r=sqrt42$
or
$r = 6.48$ $r=6.48$
Circumference= $2 π r = 2 π (6.48) = 40.72$ $2pir=2pi(6.48)=40.72$
Chord goes from $5 \frac{π}{4}$ $5pi/4$ to $4 \frac{π}{3}$ $4pi/3$ that is moves $(\frac{4}{3} - \frac{5}{4}) π = \frac{π}{12}$ $(4/3-5/4)pi=pi/12$
Therefore we can write
$2 π$ $2pi$ corresponds to $40.72$ $40.72$
$\frac{π}{12}$ $pi/12$ corresponds to $\frac{40.72}{2 π} (\frac{π}{12})$ $40.72/(2pi)(pi/12)$
$= 1.7$ $=1.7$

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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 $42 π$ $42 pi$ , 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 $42 π$ $42 pi$ , what is the length of the chord?