A circle has a chord that goes from $\frac{2 π}{3}$ $(2 pi)/3$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $120 π$ $120 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{2 π}{3}$ $(2 pi)/3$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $120 π$ $120 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-07T13:43:24

$= 1.43$ $=1.43$

Explanation:

A chord that goes from $2 \frac{π}{3}$ $2pi/3$ to $5 \frac{π}{8}$ $5pi/8$
so it travels the distance $2 \frac{π}{3} - 5 \frac{π}{8} = \frac{π}{24}$ $2pi/3-5pi/8=pi/24$ ;
or
$\frac{π}{24} \div 2 π = \frac{1}{48}$ $pi/24-:2pi=1/48$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 120 π$ $=pir^2=120pi$
or
$r^{2} = 120$ $r^2=120$
or
$r = \sqrt{120}$ $r=sqrt120$
or
$r = 10.95$ $r=10.95$
Circumference of the circle $= 2 π r = 2 (π) (10.95) = 68.83$ $=2pir=2(pi)(10.95)=68.83$
Therefore Length of the chord $= 68.83 (\frac{1}{48}) = 1.43$ $=68.83(1/48)=1.43$

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A circle has a chord that goes from $\frac{2 π}{3}$ $(2 pi)/3$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $120 π$ $120 pi$ , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from 2π3(2 pi)/3 to 5π8(5 pi) / 8 radians on the circle. If the area of the circle is 120π120 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{2 π}{3}$ $(2 pi)/3$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $120 π$ $120 pi$ , what is the length of the chord?