Answer:
12 units
Step-by-step explanation:
The angle measure in radians is 5π/6. An entire circle is 2π radians; this means the angle is
[tex]\frac{\frac{5\pi}{6}}{2\pi}\\\\=\frac{5\pi}{6}\times \frac{1}{2\pi}\\\\=\frac{5\pi \times 1}{6\times 2\pi}\\\\=\frac{5\pi}{12\pi}\\\\\=\frac{5}{12}[/tex]
of the circle.
The sector has a length of 10π units. This is 5/12 of the circumference; the formula for circumference is C = 2πr:
10π = 5/12(2πr)
Multiply both sides by 12:
12(10π) = 5(2πr)
12(10π) = 10πr
Divide both sides by 10π:
(12(10π))/(10π) = (10πr)/(10π)
12 = r
