Question 25
Luísa does experiments with a cork and a glass of water. Because of its density, a cork floats with only $60\%$ of its volume submerged in water. The cork in Luísa's experiment has the shape of a regular hexagonal prism, that is, its base is a regular hexagon, with height $3~\mathrm{cm}$ and with $2~\mathrm{cm}$ as the diameter of the circle circumscribed about the base.
a) If the cork stands "upright", as in the figure, what is the height of the part that is not submerged?
b) If the cork lies "on its side", as in the figure, what is the height of the part that is not submerged, if two of the lateral faces (the top one and the bottom one) are parallel to the water level?
a) If the cork stands "upright", as in the figure, what is the height of the part that is not submerged?
b) If the cork lies "on its side", as in the figure, what is the height of the part that is not submerged, if two of the lateral faces (the top one and the bottom one) are parallel to the water level?