The diagram shows a closed container in the shape of a cylinder with radius \(x\) cm and height \(y\) cm.
Given that the volume of the container is 32 cm\(^3\), show that the total area, \(A\) cm\(^2\), of the container is given by \(A=2\pi x^2+\dfrac{64}{x}\).[3]
Given that \(x\) can vary, find the value of \(x\) which gives a stationary value of \(A\).[3]
A company wishes to mass produce these containers using cardboard. Considering the cost of cardboard per square metre, explain why the company will be pleased with the dimensions of the container found in part (b).[2]