\(\displaystyle V_{Sphere} \ = \ \frac{4}{3} \pi r^{3}\)
\(\displaystyle \frac{dV}{dt} \ = \ 4\pi r^{2}\frac{dr}{dt}\)
\(\displaystyle Now \ \frac{dV}{dt} \ = \ 500 \ and \ when \ r \ = \ 30, \ then \ 500 \ = \ 4\pi(30^{2})\frac{dr}{dt}\)
\(\displaystyle Therefore, \ \frac{dr}{dt} \ = \ \frac{5}{36\pi} \ cm/min\)
Note: I'm assuming that n = radius, not diameter.
