A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{15 π}{8}$ $(15 pi) / 8$ 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 $\frac{15 π}{8}$ $(15 pi) / 8$ 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 · 2016-08-09T14:27:07

$= 26$ $=26$

Explanation:

A chord that goes from $\frac{3 π}{4}$ $(3pi)/4$ to $\frac{15 π}{8}$ $(15pi)/8$
so it travels the distance $\frac{15 π}{8} - \frac{3 π}{4} = \frac{9 π}{8}$ $(15pi)/8-(3pi)/4=(9pi)/8$ ;
or
$\frac{9 π}{8} \div 2 π = \frac{9}{16}$ $(9pi)/8-:2pi=9/16$ 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 $= 2 π r = 2 (π) (7.35) = 46.17$ $=2pir=2(pi)(7.35)=46.17$
Therefore Length of the chord $= 46.17 \times \frac{9}{16} = 26$ $=46.17times9/16=26$

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A circle has a chord that goes from $\frac{3 π}{4}$ $( 3 pi)/4$ to $\frac{15 π}{8}$ $(15 pi) / 8$ 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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A circle has a chord that goes from 3π4( 3 pi)/4 to 15π8(15 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 $\frac{15 π}{8}$ $(15 pi) / 8$ radians on the circle. If the area of the circle is $54 π$ $54 pi$ , what is the length of the chord?