## Calculus 8th Edition

(a)$$r=2t$$ (b)$$(V \circ r)(t)= \frac{32}{3} \pi t^3$$ This composite function represents the volume of the inflating spherical balloon in terms of time.
(a) The value of the radius of the inflating spherical balloon equals the velocity times the elapsed time. So we have $$r=2t.$$ (b)$$V=\frac{4}{3} \pi r^3$$ $$\Rightarrow \quad (V \circ r)(t)=V(r(t))=\frac{32}{3} \pi t^3$$