The length of the arc measuring 51.6 degrees is 11.4 cm.

Use proportions to convert 51.6 degrees to radians:

`51.6/180=x/pi`

where x is the value of 51.6 degrees in radians. Solve for x:

`x=((51.6)(pi))/180=0.9` radians

The arc length is equal to the angle in radians multiplied by the radius of the circle:

Arc length=`=thetar`

Solve for r and substitute 11.4 cm for arc length and 0.9 for theta.

r=11.4/0.9=12.67

**Therefore the radius of the pulley is equal to 12.7 cm.**