V = (4/3)·pi·r3
- V = volume of balloon
- r = radius of balloon
dV/dt = dV/dr · dr/dt [Chain Rule]
dV/dt = 4·pi·r2 · dr/dt
Plug in dV/dt = 10 cm3/sec and r = 20 cm and solve for dr/dt.
That will give the rate at which the radius is changing. The diameter is changing at twice the rate.