Why do scientists commonly use radius to measure size? Isn't it much more convenient to use the diameter?
Because radius is the base unit and in all cases where you use diameter you have to convert it down to be radius and essentially use diameter/2, which is radius, throughout.
area of circle=PI*r^2 not PI*(0.5*D)^2
volume of sphere = (4/3)PI*r^3 not (4/3)Pi*(0.5*D)^3
area of sphere = 4PI*r^2 not 4Pi*(0.5*D)^2
the unit circle
http://en.wikipedia.org/wiki/Unit_circle has radius=1 and not diameter=1
speed of point on rotating sphere = angularVelocity*r not angularVelocity*0.5*D
and I could go on...
You are, however, correct in that its more natural to most people to use diameter. A thing is as big as from one end to the other end. Its just not the simpler way to calculate things, and therefore radius becomes a standard in science.