12. A company makes drinks containers out of metal, The containers are modelled as closed cylinders with base radius rem and height hem and the capacity of each container is 355 cm The metal used for the circular base and the curved side costs 0.04 pence/cm for the circular top costs 0.09 pence/cm Both metals used are of negligible thickness. (a) Show that the total cost, C pence, of the metal for one container is given by 28.4 C=0.13xr+ (4) (b) Use calculus to find the value of r for which C is a minimum, giving your answer to 3 significant figures. (4) (c) Using J.2 prove that the cost is minimised for the value of r found in part (b). (2) (d) Hence find the minimum value of C, giving your answer to the nearest integer. (2)