A tin has a fitting cylindrical lid which overlaps its cylindrical body by 5 cm. When completely closed, it has base radius x cm and height y cm, as shown in the diagram. The body and the lid are made from thin metal sheet such that the difference in their radii is negligible. The total area of metal sheet used to make the tin and its lid is 400z cm². 5 cm y cm x cm Show that the volume V cm³ of the tin is given by V = Tx(200–x² – 5x). If x varies, find by differentiation the values of x and y for which V has its maximum value. 20 55 [x = = y = 3

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