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

Measure of the sector arc = 229.09°

Explanation:

Area of circle = πr²

`\texttt{Area of sector = }(\pi r^2)/(2\pi)* \theta`

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

`((\pi r^2)/(2\pi)* \theta )/(\pi r^2)=(7)/(11)\\\\(\theta )/(2\pi)=(7)/(11)\\\\\theta =(14\pi)/(11)=229.09^0`

Measure of the sector arc = 229.09°

Answer 2

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°