Need Help on ONE related rate problem?

Question

Can you please show me how to do it step by step. Thanks! A good answer will earn 10 points.

How fast does the radius of a spherical soap bubble change when you blow air into it at the rate of 15 cubic centimeters per second?

Answer 1

V = (4/3)πr^3
dV/dt = (dV/dr) (dr/dt)
(dr/dt) = (dV/dt) / (dV/dr)
dV/dr = 4πr^2
(dr/dt) = (dV/dt) / (4πr^2)
(dr/dt) = (15) / (4πr^2)
(dr/dt) ≈ 1.193662 / r^2
Evaluating with r in cm, the rate will be cm/s.