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\includegraphics[max width=\textwidth, alt={}, center]{567c3d72-c633-4ae0-8605-f63f93d718c4-08_512_460_258_772}
\includegraphics[max width=\textwidth, alt={}, center]{567c3d72-c633-4ae0-8605-f63f93d718c4-08_462_85_260_1279} The diagram shows a solid cone which has a slant height of 15 cm and a vertical height of \(h \mathrm {~cm}\).

1. Show that the volume, \(V \mathrm {~cm} ^ { 3 }\), of the cone is given by \(V = \frac { 1 } { 3 } \pi \left( 225 h - h ^ { 3 } \right)\).
   [0pt] [The volume of a cone of radius \(r\) and vertical height \(h\) is \(\frac { 1 } { 3 } \pi r ^ { 2 } h\).]
2. Given that \(h\) can vary, find the value of \(h\) for which \(V\) has a stationary value. Determine, showing all necessary working, the nature of this stationary value.