A ship with a displacement of 8,200 tonnes and a length of 90 m is floating in sea water with a density of 1.024 t/m³. The half-ordinates of the waterplane area at equal intervals are: 0, 2.61, 3.68, 4.74, 5.84, 7.00, 7.30, 6.47, 5.35, 4.26, 3.16, 1.88, and 0 m. Calculate: (16)

(i) Calculate the Waterplane Area using Simpson's First Rule.

(ii) Calculate the TPC (Tonnes per Centimetre Immersion) in sea water.

(iii) Find the change in mean draught when the ship moves from sea water of density 1.024 t/m³ into river water with a density of 1.005 t/m³.