A manufacturer needs a metal tank to hold 1331x m of paint. It is to have a circular base and to be open at the top. The side of the tank is to be made by a rectangle of steel 'rolled around" to form a cylinder that has the same circumference as the base. Find the dimensions that minimise the materials required to make the tank, and so reduce the cost of making the tank. (1) What is the area and circumference of a circle? (2) What is the volume of a cylinder? (3) Use the answers in (1) and (2) to find the function for the area of metal required to make the tank. (The total area for the metal base and rectangle used for the side only). (4) Use calculus to find the dimensions (radius and height) that minimise the metal used, Show all working. (5) Demonstrate that these dimensions do minimise (and don't maximise) the metal used. Show all working