A buoy is made from a steel tube 4meters long and 0.5meters in radius, with a welded one half-sphere at each end. Knowing the weight of the buoy is 3630N

*) Find the height of immersion of the buoy if it is immersed in fresh water.

The buoyancy force is directed vertically upwards when a body is immersed in a liquid (allowing it to float). This force corresponds to the weight of the liquid displaced.
For example, an object immersed in water (with a density of 1000 kg/m3) undergoes a buoyancy of 9810N for each cubic meter of its volume submerged (that is to say 9 • 81m/s2 1000 kg/m3 • 1m3 = 9810N).

Question

A buoy is made from a steel tube 4meters long and 0.5meters in radius, with a welded one half-sphere at each end. Knowing the weight of the buoy is 3630N

*) Find the height of immersion of the buoy if it is immersed in fresh water.

The buoyancy force is directed vertically upwards when a body is immersed in a liquid (allowing it to float). This force corresponds to the weight of the liquid displaced. 
For example, an object immersed in water (with a density of 1000 kg/m3) undergoes a buoyancy of 9810N for each cubic meter of its volume submerged (that is to say 9 • 81m/s2 1000 kg/m3 • 1m3 = 9810N).

anonymous · Answer

I've calculated the volume of the buoy (volume of cylinder + volume of sphere), which equals 3.66519 cubic meters
$$V =(π×〖0.5m〗^2×4m)+ ((4π〖0.5〗^3)/3)	$$

anonymous · Answer

$$Buoy's Buoyancy force = 9810N * 3.66519 = 35955.5139 Newtons$$

anonymous · Answer

Not sure if useful, but I've calculated the Buoy's mass in kg
$$Buoy's Mass = 3630 Newtons  (N = mg, N/g=m, 3630N/9.81m/s ^{2}=370.03kg$$

anonymous · Answer

and from here I'm stuck, I know I should be using integrals but I'm not sure how to go about it to find the immerged height

anonymous · Answer

will pay for help. lol