a spherical balloon is filled with water. if the water is leaking out at a rate of 2 cm^3/min, find the rate at which the radius is changing when the volume is v=1000cm^3?

Answer 1

v = 4/3 pi r^3
when v = 1000, r = ∛(3000/(4pi))

dv/dt = 4 pi r^2 dr/dt

Now just plug in your values for dv/dt and r to get dr/dt.