Mathematics

Problem

Let

V(h)

denote the volume (in m

^{3}

) of liquid in a storage tank as a differentiable function of the liquid height

h

(in m). If liquid enters the tank at a constant rate

\dfrac{dV}{dt}=k\,

^{3}

/min, determine

\dfrac{dh}{dt}

in terms of

k

and

V'(h)=\dfrac{dV}{dh}