Air is being pumped into a spherical balloon at a rate of 2 cubic meters per minute. At what rate is the radius changing when the volume of the balloon is 36pi cubic meters?

Answer 1

V = (4/3)π r^3
when V = 36π
36π = (4/3)π r^3
27 = r^3
r = 3 m

dV/dt = 4π r^2 dr/dt
2 = 4π (9)dr/dt
dr/dt = 2/(36π) m/min
= appr .01768 m/min