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

option A: 120°

Explanation:

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