A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{19 π}{12}$ $(19 pi) / 12$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{19 π}{12}$ $(19 pi) / 12$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-07T13:33:52

$= 27.2$ $=27.2$

Explanation:

A chord that goes from $\frac{π}{3}$ $pi/3$ to $19 \frac{π}{12}$ $19pi/12$
so it travels the distance $19 \frac{π}{12} - \frac{π}{3} = 5 \frac{π}{4}$ $19pi/12-pi/3=5pi/4$ ;
or
$5 \frac{π}{4} \div 2 π = \frac{5}{8}$ $5pi/4-:2pi=5/8$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 48 π$ $=pir^2=48pi$
or
$r^{2} = 48$ $r^2=48$
or
$r = \sqrt{48}$ $r=sqrt48$
or
$r = 6.93$ $r=6.93$
Circumference of the circle $= 2 π r = 2 (π) (6.93) = 43.53$ $=2pir=2(pi)(6.93)=43.53$
Therefore Length of the chord $= 43.53 (\frac{5}{8}) = 27.2$ $=43.53(5/8)=27.2$

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A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{19 π}{12}$ $(19 pi) / 12$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from π3( pi)/3 to 19π12(19 pi) / 12 radians on the circle. If the area of the circle is 48π48 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 $\frac{π}{3}$ $( pi)/3$ to $\frac{19 π}{12}$ $(19 pi) / 12$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?