Molten plastic is injected into the centre of a circular mold of constant height, H, through a small hole. The rate of injection is such that the radius of the plastic inside the mould increases so that

Question

Molten plastic is injected into the centre of a circular mold of constant height, H, through a small hole. The rate of injection is such that the radius of the plastic inside the mould increases so that 
r(t)= 3t^2 -2t^3 where the mold has maximum radius of one unit. Compute the rate of change of volume of plastic in the mold, V (t), given that V = H(pie)r^2. At what time is the mold filling fastest and what is the value of dV/dt at that time?