We enter given parameters into our volume formula.

Input := 


v[t_] = vol[t]/.{k->.4836,v0->300}

Output =


    1/3                 1/3   3

(300    - 0.1612 (36 Pi)    t)

Input := 


solt = Solve[v[t]==0,t]

Output =


{{t -> 8.58733}, {t -> 8.58733}, {t -> 8.58733}}

Input := 


endTime = t/.solt[[1]]

Output =


8.58733

Input := 


Plot[v[t],{t,0,endTime},PlotRange->{0,300}]

Output =


-Graphics-

Thus we can determine how long it takes the capsule to drop from 300 ml to 150 ml, i.e half its volume. It appears to be 1.77 min.