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Q7. a) An open tank is to be in the shape of a triangular prism, as shown in Fig Q7(a).

The triangular cross - section of the tank is right - angled and isosceles, with equal sides of length x cm.

The tank has a length of I cm and when full of water it is to have a wetted surface area of 10800 cm2

Determine EACH of the following for the tank:

(i) an expression, in terms of x, of its capacity in cm3; (5)

(ii) the value of x which maximises its capacity; (5)

(iii) the maximum capacity in litres. (2)

b) Determine the first and second derivatives of the function:

C = 2r + 5/r (4)