A 25 degree arc of a circle has an area of 50m2. What is the circumference of the circle?

Question

I have searched everywhere for an answer to this and cannot find help.

Answer 1

The formula for finding the area of a sector with a given arc is:

 

A=θ/360•πr²

 

Since you know the area and the arc measure, you can solve this equation for the radius, which will allow you to find the circumference.

 

50=25/360•πr²

18000=25πr²

720=πr²

229.18=r²

15.14=r

 

The radius is 15.14 m, so the circumference is 2πr = 2π(15.14) =95.13 m