Question

If the ratio of a circles sector to its total area is 7/11 what is the measure of its sector arc

Answer 1

The sector area is proportional to the arc measure. The arc measure is the same fraction of 2π radians or 360° as the area is to the area of the whole circle. That fraction is given here as 7/11.

In radians, the arc will be
   (7/11)*2π = 14π/11 radians
In degrees, the arc will be
   (7/11)*360° = 229 1/11°

Answer 2

Answer:

Measure of the sector arc = 229.09°

Step-by-step explanation:

Area of circle = πr²

$\texttt{Area of sector = }\frac{\pi r^2}{2\pi}\times \theta$

We have ratio of a circles sector to its total area is 7/11.

$\frac{\frac{\pi r^2}{2\pi}\times \theta }{\pi r^2}=\frac{7}{11}\\\\\frac{\theta }{2\pi}=\frac{7}{11}\\\\\theta =\frac{14\pi}{11}=229.09^0$

Measure of the sector arc = 229.09°