A spherical balloon is filled with gas at a rate of 4 cm 3 / s. at what rate is the radius r changing with with respect to time when the volume v = 36 π cm 3?

The volume of the sphere is given by V = 4/3 * pie * r^3. We seek dr/dt that the rate of change of the radius with respect to time.

V = 4/3 * pie * r^3

Since we know the rate at which the volume changes wrt time. We can plug it in to find dr/dt.

dV/dt = 36pie. But dV/dt = 4/3 * pie * 3r^2 * dr/dt

So we have that dr/dt = (dV/dt) / 4/3 * pie * 3r^2

So dr/dt = (36pie) / 4/3 * pie * 3 (4) ^2

dr/dt = 113.112 / 201.0864 = 0.5624