calculus help

Question #1 
Determine whether a cylinder of radius 4 in, height 10 in, and weight 15 lb. can float in a deep pool of water of weight density 62.5 lb/ft3. Let h denote the length (in feet) of the submerged portion of the cylinder at equilibrium. With r = 1/3 ft. Please give a summary of how this works,

Question #2
Determine an expression for the motion of the cylinder described in my first question (cylinder of radius 4 in, height 10 in, and weight 15 lb, water density 62.5 lb/ft3, r =1/3 ft.) if is released with 20% of its length above the water line with a veolocity of 5 ft/sec in a downward direction. Please give a summary of how this works,

Question #4
Find the expression for the motion of the cylinder described in my Question 3 (cylinder of radius 3 in, height 20 in, and a weight of 5 ╥ lb. that is floating with its axis vertical in a deep pool of water of weight density 62.5lb/ft3. ) if it is disturbed from its equilibrium position by submerging an additional 2 in of height below the water line and with a velocity of 1 ft/sec in the downward direction. Please give a summary of how this works,