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The question doesn't state whether its subtended at the center or circumference, but I not sure if it matters

The sector a circle subtended by an angle of $22.5$ degrees has an area of $\frac{9\pi}{4}$ squared meters.
I have never done one of these problems before but after searching the internet I found the formula $$s=r\theta$$

though this is the formula for the arc length and I'm not sure if you can find the diameter from this formula.

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    $\begingroup$ Note $22.5=360/16$ $\endgroup$ – J. W. Tanner May 14 at 22:16
  • $\begingroup$ I have never encountered a problem like this, could I get one more hint? $\endgroup$ – Eric Brown May 14 at 22:24
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    $\begingroup$ The area of a circular sector is the circle's area times the ratio of the angle and $360^o$ $\endgroup$ – J. W. Tanner May 14 at 22:34
  • $\begingroup$ So the equation should be $\frac{9\pi}{4}=Area * \frac{360}{16}$? $\endgroup$ – Eric Brown May 14 at 22:49
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    $\begingroup$ $\frac{9\pi}4=Area\; of circle \times \frac {22.5}{360}$ $\endgroup$ – J. W. Tanner May 14 at 22:56
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The area of a circular sector is the circle's area times the ratio of the angle and $360^o$.

In this case, that ratio is $22.5^o/360^o=1/16$.

Therefore the area of the circle is $16\times\dfrac{9\pi}4 $m$^2 = 36\pi$ m$^2.$

The area of a circle is $\pi r^2$, so in this case $r^2=36$ m$^2,$ so $r=6$ m.

The diameter is twice the radius: $d=2r=2\times6 $ m $ =12$ m.

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