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Q8. A dam is to be built to contain water in a new reservoir.

Relative to axes, as shown in Fig Q8, the sides of the walls can be represented by parts of the graphs of y = 4x, 0 ≤ x ≤ 5, and y = 36 - 1/4 x², 8 ≤ x ≤ 12.

The shaded area represents the constant cross–section of the dam wall.

Calculate EACH of the following for the dam wall, given that the dimensions are in metres:

(a) its height; (2)

(b) its cross - sectional area, using integral calculus; (12)

(c) its volume, given that it is 360m in length. (2)