The radius r (in meters) of an inflating spherical balloon after t seconds is modeled by
r(t)=0.10t3/2,t≥0.
The volume V (in cubic meters) of the balloon satisfies V(t)=34πr(t)3.
(a) Express V explicitly as a function of t.
(b) Determine V′(t).
(c) Evaluate V′(9), including correct units.
(d) Interpret the value found in part (c) in the context of the balloon’s inflation.
(e) Using your result from part (c), estimate the additional volume of air, in cubic meters, that enters the balloon between t=9 seconds and t=9.1 seconds. Justify your approximation.