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Q7. A closed right cylindrical tank, of diameter d metres and volume 5 cubic metres, is to be fabricated from surplus sheet steel.

The seam of the cylindrical shell is welded and then the circular ends are welded to the shell as shown in Fig Q7.

The cost, C pounds, of welding the seams is given by the formula:

C = 80πd√(800/(πd²))

Calculate EACH of the following for the tank:

(a) the diameter that minimises the cost of welding; (6)

(b) the minimum cost of the welding; (3)

(c) the height of the tank for minimum welding cost; (3)

(d) the cost of the welding per metre length. (4)