The diagram shows a container used to contain a chocolate product. It is made up of a cone fixed to the top of a right circular cylinder of radius \(r\) cm and height \(h\) cm. The slant height of the cone is \(2r\) cm.
Given that the volume of the cylindrical part is \(108\pi\text{ cm}^3\), express \(h\) in terms of \(r\).[1]
Show that the total surface area, \(A\text{ cm}^2\), of the container is given by \(A=3\pi\left(r^2+\dfrac{72}r\right)\).[2]
Given that \(r\) can vary, find the value of \(r\) for which \(A\) has a stationary value and explain why this value of \(r\) gives the minimum value of surface area.[5]
For aesthetic purposes, a shop owner would only display the container in his shop only if the height of the container is less than 35 cm and has minimum surface area. Determine whether the container can be displayed in the shop.[2]