A chord with a length of $9$ $9$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on a circle. What is the area of the circle?

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A chord with a length of $9$ $9$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-01-03T21:59:10

About 14872.2800 $u n^{2}$ $un^2$

Explanation:

The formula used to find the length of a chord is $2 r \cdot sin (\frac{θ}{2}) = l$ $2r*sin(theta/2)=l$ where $r$ $r$ is the radius, $θ$ $theta$ is the measure of the arc, and $l$ $l$ is the length of the chord.
One circle has 2 $π$ $pi$ radians. If you take the difference of $\frac{π}{12}$ $pi/12$ and $\frac{π}{8}$ $pi/8$ , you should get $\frac{π}{24}$ $pi/24$ . This is your $θ$ $theta$ . Now you can plug in what you know and solve for $r$ $r$ . $r \approx$ $r~~$ 68.80405. You can plug that into the equation for the area of a circle, $A = π r^{2}$ $A=pir^2$ which yields about 14872.2800.

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A chord with a length of $9$ $9$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on a circle. What is the area of the circle?

1 Answer

Explanation:

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A chord with a length of $9$ $9$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{8}$ $pi/8$ radians on a circle. What is the area of the circle?