A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{11 π}{8}$ $(11 pi) / 8$ radians on the circle. If the area of the circle is $64 π$ $64 pi$ , what is the length of the chord?

Question

A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{11 π}{8}$ $(11 pi) / 8$ radians on the circle. If the area of the circle is $64 π$ $64 pi$ , what is the length of the chord?

1 Answer

Impact of this question

1467 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-24T08:08:42

The length of the chord is $= 15.2$ $=15.2$

Explanation:

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

$θ = \frac{11}{8} π - \frac{1}{6} π = \frac{66}{48} π - \frac{8}{48} π = \frac{58}{48} π = \frac{29}{24} π$ $theta=11/8pi-1/6pi=66/48pi-8/48pi=58/48pi=29/24pi$

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

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

Here, $A = 64 π$ $A=64pi$

So,

$π r^{2} = 64 π$ $pir^2=64pi$

$r^{2} = 64$ $r^2=64$

$r = 8$ $r=8$

The length of the chord is

$l = 2 \cdot r sin (\frac{θ}{2})$ $l=2*rsin(theta/2)$

$= 2 \cdot 8 \cdot sin (\frac{29}{48} π)$ $=2*8*sin(29/48pi)$

$= 15.2$ $=15.2$

Science

Math

Humanities

... and beyond

A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{11 π}{8}$ $(11 pi) / 8$ radians on the circle. If the area of the circle is $64 π$ $64 pi$ , what is the length of the chord?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle has a chord that goes from π6( pi)/6 to 11π8(11 pi) / 8 radians on the circle. If the area of the circle is 64π64 pi , what is the length of the chord?

1 Answer

Explanation:

Related questions

Impact of this question

A circle has a chord that goes from $\frac{π}{6}$ $( pi)/6$ to $\frac{11 π}{8}$ $(11 pi) / 8$ radians on the circle. If the area of the circle is $64 π$ $64 pi$ , what is the length of the chord?