Question

If radius of a circle is decreasing at the rate of 3cm/s find rate of change of circumference when r=2

Answer 1

C = 2πr
dC/dt = 2π dr/dt

Now just plug and chug. You will note that dC/dt does not depend on r.

Answer 2

OOBleck is correct, but just to be clear (and this answer is about a year late).
So plugging and chugging... 2 Pi times -3 cm/sec (negative since it's decreasing) Gives -6 Pi ... this is the "rate of change" of C. it is -6 Pi at r=2, and -6 Pi at any other r. so, it is independent of r. However, that does not tell us what the circumference actually is at any r. But without the derivative, we know C = 2 Pi r. at r=2, C = 4 Pi cm.