Given the width of the lawnmower is 2.5 feet and the length of the rope is 25 feet, calculate the radius (R) of the pole that will produce a perfect lawn

For the perfectly mowed lawn, after one revolution, you want the lawnmower to be exactly one lawnmower's width closer to the pole. This implies that one lawnmower width should wrap around the circumference of the pole every revolution. So for this lawnmower we want:

2πR=2.5

⇒R=2.5/2π

R=0.39789 ft