Expert: Steve Holleran - 2/25/2008

Question
A dog is tied to a 40 foot rope that swings 120 degrees. How much area can the dog cover?

Answer
Hi Amy,

Okay, so basically we have a circular sector with a radius of 40 ft and a central angle of 120 deg = 2pi/3 radians.

The formula for the area of a complete circle of r=40 is
 
                      A = pi *  r^2 = 1600pi

so since 120 = 1/3 of 360 degrees, we want 1/3 of this area:

                    A = 1/3 * 1600pi = 1675.516 sq ft.


Hope this helps out.

Steve