A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meter per minute At what rate is the diameter increasing when the diameter is 12 meter?

V = 4/3*pi*r^3dV/dt = 4/3*pi*3*r^2*dr/dt = 4*pi*r^2*dr/dt

Therefore dV/dt = 5 => 4*pi*r^2*dr/dt = 5

therefore dr/dt = 5/(4*pi*r^2)

Diameter = 12 metres => radius = 6 metres

So dr/dt = 5/(4*pi*36) = 0.01105 metres per minute.

diameter = 2*radius => rate of change of diameter = 0.2210 metres per minute.