A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{13 π}{8}$ $(13 pi) / 8$ radians on the circle. If the area of the circle is $54 π$ $54 pi$ , 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 $\frac{13 π}{8}$ $(13 pi) / 8$ radians on the circle. If the area of the circle is $54 π$ $54 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-10T21:05:47

$= 20.2$ $=20.2$

Explanation:

A chord that goes from $\frac{3 π}{4}$ $(3pi)/4$ to $\frac{13 π}{8}$ $(13pi)/8$
so it travels the distance $\frac{13 π}{8} - \frac{3 π}{4} = \frac{7 π}{8}$ $(13pi)/8-(3pi)/4=(7pi)/8$ ;
or
$\frac{7 π}{8} \div 2 π = \frac{7}{16}$ $(7pi)/8-:2pi=7/16$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 54 π$ $=pir^2=54pi$
or
$r^{2} = 54$ $r^2=54$
or
$r = \sqrt{54}$ $r=sqrt54$
or
$r = 7.35$ $r=7.35$
Circumference of the circle $= 2 π r = 2 (π) (7.35) = 46.18$ $=2pir=2(pi)(7.35)=46.18$
Therefore Length of the chord $= 46.18 \times \frac{7}{16} = 20.2$ $=46.18times7/16=20.2$

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{13 π}{8}$ $(13 pi) / 8$ radians on the circle. If the area of the circle is $54 π$ $54 pi$ , what is the length of the chord?

1 Answer

Explanation:

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Science

Math

Humanities

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A circle has a chord that goes from 3π4( 3 pi)/4 to 13π8(13 pi) / 8 radians on the circle. If the area of the circle is 54π54 pi , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{13 π}{8}$ $(13 pi) / 8$ radians on the circle. If the area of the circle is $54 π$ $54 pi$ , what is the length of the chord?