Consider a closed storage tank S with walls given by the curved surfaces x = y^2; z ≥ 0 and x = 2-y^2; z ≥  0; floor at z = 0, and roof is part of the plane x + 2y + 2z = 6: (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral.

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