Related rates : filling a cone

Problem Formulation :

Consider an inverted cone with height 20 meters and radius 20 meters. Assume water enters at a rate of 2 π meters^3 /sec. How fast is the height increasing when there is 9 π meters^3 of water in the cone?

Functions :

V[r_] := (1/3) Pi r^3;
radius[vol_] := (3 vol / Pi)^(1/3);
volume[t_] := 2 Pi t;
line[t_,height_] := If[Abs[x] ≤ height, height, GoEphs];
heightfn[x_,t_] := If[x ≥ 0 && x < radius[volume[t]], -5, GoEphs];

boundary[x_] := Abs[x];
Manipulate[Plot[{boundary[x], line[x,radius[volume[t]]], heightfn[x,t]}, {x,-20,20}, Epilog -> {
{PointSize[.025], Point[{-radius[volume[t]],radius[volume[t]]}]},{PointSize[.025], Point[{radius[volume[t]],radius[volume[t]]}]},
{PointSize[.025], Point[{radius[volume[t]],-5}]}}], {t,0,1200}]

Related rates : separating cars

Problem Formulation :

At time 0, car A leaves the origin traveling at 40 mph along the positive x-axis, while car B leaves the origin traveling at 30 mph along the positive y-axis. How fast are the cars separating at one hour?

cara[t_] := 40 t;
carb[t_] := 30t;
dist[t_] := Sqrt[cara[t]^2+carb[t]^2];
carline[x_,t_] := If[0 ≤ x && x ≤ cara[t], -(carb[t]/cara[t]) x +carb[t], GoEphs];
cardistfn[x_,t_] := If[x ≥ 0 && x < dist[t], -10, GoEphs];
Manipulate[Plot[{carline[x,t], cardistfn[x,t]}, {x,0,60}, PlotRange -> {-12,60},  Epilog -> {
{PointSize[.025], Point[{0,carb[t]}]},
{PointSize[.025], Point[{cara[t],0}]},
{PointSize[.025], Point[{dist[t],-10}]}
}], {t,0,1}]