Question

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 ?

Answer 1

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