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Q Liquid is being poured into a parabolic bowl at a constant rate of $60\pi c{m}^3/s$. The volume of the bowl is given by $V=(1/2)\pi x^4$, where the equation of the parabola is $y=x^2$, where y is the height of liquid in the bowl. Find the rate of increase of the height of the liquid in the bowl when the height is 10 centimetres.

A We can write Volume $V=(1/2)\pi x^4=(1/2)\pi y^2$

$\frac{dV}{dt}=\pi y\frac{dy}{dt}$

$\frac{dV}{dt}$ is $60\pi$.

So, when y=10, we can evaluate $\frac{dy}{dt}$ which is the rate of change, which evaluates to be 6cm/s.