(i) Given \(V = \frac{1}{3} \pi r^2 h\) and \(h + r = 18\), we can express \(h\) as \(h = 18 - r\). Substituting this into the volume formula gives:

\(V = \frac{1}{3} \pi r^2 (18 - r) = \frac{1}{3} \pi r^2 \times 18 - \frac{1}{3} \pi r^3\)

\(V = 6\pi r^2 - \frac{1}{3} \pi r^3\)

(ii) To find the stationary value, differentiate \(V\) with respect to \(r\):

\(\frac{dV}{dr} = 12\pi r - \pi r^2\)

Set \(\frac{dV}{dr} = 0\):

\(12\pi r - \pi r^2 = 0\)

\(\pi r (12 - r) = 0\)

\(r = 12\) (since \(r = 0\) is not a valid solution for a cone)

To confirm it's a maximum, find the second derivative:

\(\frac{d^2V}{dr^2} = 12\pi - 2\pi r\)

Substitute \(r = 12\):

\(\frac{d^2V}{dr^2} = 12\pi - 24\pi = -12\pi\)

Since \(\frac{d^2V}{dr^2} < 0\), the stationary point is a maximum.

(iii) Substitute \(r = 12\) into \(h = 18 - r\):

\(h = 6\)

Maximum volume \(V = \frac{1}{3} \pi (12)^2 (6) = 288\pi\) or approximately 905 cm³.