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

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Answer 1 · 2017-06-24T12:28:12

The length of the chord is $= 2 \sqrt{15} = 7.75$ $=2sqrt15=7.75$

The angle subtended by the chord at the center of the circle is

$θ = \frac{4}{3} π - \frac{1}{3} π = \frac{3}{3} π = π$ $theta=4/3pi-1/3pi=3/3pi=pi$

The chord is the diameter of the circle

Let the radius of the circle be $= r$ $=r$

The area of the circle is $A = π r^{2}$ $A=pir^2$

Here, $A = 15 π$ $A=15pi$

So,

$π r^{2} = 15 π$ $pir^2=15pi$

$r^{2} = 15$ $r^2=15$

$r = \sqrt{15}$ $r=sqrt15$

The length of the chord is

$l = 2 \cdot \sqrt{15} = 7.75$ $l=2*sqrt15=7.75$

A circle has a chord that goes from π3( pi)/3 to 4π3(4 pi) / 3 radians on the circle. If the area of the circle is 15π15 pi , what is the length of the chord?