Question

Consider circle C below, where the central angle is measured in radians.

Answer 1

Answer:

12, just took the test

Step-by-step explanation:

Answer 2

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

$\frac{\frac{5\pi}{6}}{2\pi}\\\\=\frac{5\pi}{6}\times \frac{1}{2\pi}\\\\=\frac{5\pi \times 1}{6\times 2\pi}\\\\=\frac{5\pi}{12\pi}\\\\\=\frac{5}{12}$

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