+624 A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?
+9664 Recall the following formula:
The area of a sector with radius r and central angle \(\theta^\circ\) is \(\dfrac{\theta}{360} \cdot \pi r^2\).
Using the formula, we have
\(\dfrac{83}{360} \cdot \pi r^2 = 60 \pi\)
This means
\(r^2 = \dfrac{360 \cdot 60}{83} = \dfrac{21600}{83}\)
\(r = \sqrt{\dfrac{21600}{83}} \approx 16.13\)
+9664 Recall the following formula:
The area of a sector with radius r and central angle \(\theta^\circ\) is \(\dfrac{\theta}{360} \cdot \pi r^2\).
Using the formula, we have
\(\dfrac{83}{360} \cdot \pi r^2 = 60 \pi\)
This means
\(r^2 = \dfrac{360 \cdot 60}{83} = \dfrac{21600}{83}\)
\(r = \sqrt{\dfrac{21600}{83}} \approx 16.13\)
