There is no equation for the "scale factor" of a sphere. If I assume you to mean how the volume increases with radius then you would use the volume equation for a sphere and calculate volume based on corresponding radii. You could then divide the resultant volumes to give a percentage or factor of how much larger or small one sphere is than another. You'll see that a small change in radius causes a large change in volume due to the volume being a cubic factor of the radius.
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scale factor
12r = p
Tautologically!
The equation of a sphere with radius r, centered at (x0 ,y0 ,z0 ) is (x-x0 )+(y-y0 )+(z-z0 )=r2
Scale factor and perimeter are related because if the scale factor is 2, then the perimeter will be doubled. So whatever the scale factor is, that is how many times the perimeter will be enlarged.