Determine if a cylinder of length 360 mm and diameter 80 mm can float vertically in water (density 1000 kg/m3).

To determine if the cylinder can float vertically in water, we need to calculate its metacentric height ($GM$). If $GM > 0$, it is stable and can float vertically. If $GM < 0$, it is unstable and will not float vertically.

Given data:
Total length of cylinder, $L = 360 \text{ mm} = 0.36 \text{ m}$
Diameter of cylinder, $D = 80 \text{ mm} \implies \text{Radius}, R = 40 \text{ mm} = 0.04 \text{ m}$
Density of water, $\rho_{\text{water}} = 1000 \text{ kg/m}^3$

The cylinder