A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?

1 Answer

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Answer 1 · 2016-07-29T21:07:03

$= \frac{π}{3}$ $=pi/3$

Explanation:

Chord has traveled $\frac{π}{2}$ $pi/2$ to $\frac{2 π}{3}$ $(2pi)/3$ radians
or
$\frac{π}{6}$ $pi/6$ radians
$= \frac{180}{6}$ $=180/6$ Degrees
$= 30^{\circ}$ $=30^@$

Circumference of the circle with area= $4 π$ $4pi$ is also $4 π$ $4pi$
So Length of the chord can be derived as follows :
$360^{\circ}$ $360^@$ correspond to $4 π$ $4pi$
$\frac{π}{6}$ $pi/6$ radians or $30^{\circ}$ $30^@$ will correspond to $\frac{4 π}{360}$ $(4pi)/360$ x30
$= \frac{π}{3}$ $=pi/3$

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $4 π$ $4 pi$ , what is the length of the chord?