Final answer:
The height of water in the cylindrical vessel is approximately 13.5 cm.
Step-by-step explanation:
To find the height of water in the cylindrical vessel, we need to find the volume of water transferred from the hemispherical bowl to the cylindrical vessel.
The volume of water in the hemispherical bowl is half the volume of a sphere, given by V = (2/3)πr³, where r is the radius of the bowl.
The volume of the cylindrical vessel is given by V = πr²h, where r is the radius of the vessel and h is the height of the water in the vessel.
Equating the two volumes, we have (2/3)π(9 cm)³ = π(6 cm)²h.
Solving for h, we find that the height of water in the cylindrical vessel is approximately 13.5 cm.