Final answer:
To find the depth of water in the cylindrical container, you need to calculate the volume of water in the spherical container and then find the corresponding depth in the cylindrical container.
Step-by-step explanation:
To find the depth of water in the cylindrical container, we need to calculate the volume of water in the spherical container and then find the corresponding depth in the cylindrical container.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. In this case, the radius is half the diameter, so r = 15/2 cm = 7.5 cm.
Substituting the values into the formula, we get V = (4/3)π(7.5)^3 = 1767.14 cm³.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. In this case, the radius is half the diameter, so r = 12/2 cm = 6 cm.
Substituting the values into the formula, we get 1767.14 cm³ = π(6)^2h.
Solving for h, we divide both sides of the equation by π(6)^2 and find h = 1767.14 / (π(6)^2) ≈ 15.59 cm.
Therefore, the depth of water in the cylindrical container is approximately 15.59 cm.