Given the volume function \(V = 243 - \frac{1}{3}(9-x)^3\), we need to find \(\frac{dx}{dt}\) when \(x = 4\).

First, differentiate \(V\) with respect to \(x\):

\(\frac{dV}{dx} = (9-x)^2\).

Substitute \(x = 4\) into \(\frac{dV}{dx}\):

\(\frac{dV}{dx} = (9-4)^2 = 25\).

We know \(\frac{dV}{dt} = 3.6\) m³/hour.

Using the chain rule, \(\frac{dV}{dt} = \frac{dV}{dx} \cdot \frac{dx}{dt}\).

So, \(3.6 = 25 \cdot \frac{dx}{dt}\).

Solving for \(\frac{dx}{dt}\):

\(\frac{dx}{dt} = \frac{3.6}{25}\) m/hour.

Convert \(\frac{dx}{dt}\) to cm/min:

\(\frac{dx}{dt} = \frac{3.6}{25} \times 100 \div 60 = 0.24\) cm/min.