Question

If the ratio of a circle's sector to its total area is 1/3, what is the measure of
its sector's arc?
A. 120 degrees
B. 250 degrees
C. 180 degrees
O D. None of the above

Answer 1

Answer:

option A:  120°

Step-by-step explanation:

$Area \ of \ circle = \pi r^2\\\\Area \ of \ sector = \pi r^2 \frac{ \theta}{360}\\\\Ratio \ of \ sector \ to \ circle = \frac{1}{3}\\\\That is, \\\frac{1}{3} = \frac{\pi r^2 \frac{\theta}{360}} {\pi r^2}\\\\\\\frac{1}{3} = \frac{\theta}{360} \\\\\frac{360}{3} = \theta\\\\120 = \theta$