3. (a) Obtain the centre of pressure of any plane area. OR (b) A solid octant of the sphere is immersed with a plane face in the surfaces. Prove that the resultant pressure on the curved surface is (1+) times the weight of the water contained in it. 4. (a) Prove that for an ellipsoid the surface of floatation and buoyancy are similar ellipsoids. OR (b) Find the surface of buoyancy and surface of floating for a cylinder of any section floating in a liquid with one end immersed.