A 20-cm diameter, 60-cm high vertical cylindrical container is partially filled with 50- cm high liquid whose density is 850 kg/m3. Now the cylinder is rotated at a constant speed. If the rotational speed at which the liquid will start spilling from the edges of the container is 189.16 rpm, determine the following:

a. The height of free-surface along the axis of rotation.
b. The height of free surface at r= 5 cm and 7.5 cm
c. The pressure of the free surface at the edge of the container if the pressure air space in the tank is 1 atm.