Question

the volume v of a right circular cylinder of radius r and heigh h is V = pi r^2 h

1. how is dV/dt related to dr/dt if h is constant and r varies with time?
2. how is dv/dt related to dh/dt if r is constant and h varies with time?
3. how is dV/dt related to dh/dt and dr/dt if both h and r vary with time?

Answer 1

1) dV/dt=pi*h*d(r^2)/dt=2*pi*h*r*dr/dt

Answer 2

2)dV/dt=pi*r^2*dh/dt

3)dV/dt=pi[2r*h*dr/dt+r^2*dh/dt)