In a cylindrical vessel, the liquid level reaches 8 cm. At what height will the liquid level be if it is poured

In a cylindrical vessel, the liquid level reaches 8 cm. At what height will the liquid level be if it is poured into a second vessel, the diameter of which is 2 times the first?

Let the diameter of the smaller vessel be D cm, then, by condition, the diameter of the larger vessel is 2 * D cm.

The desired height of the liquid in the larger vessel is denoted by h cm.

The volume of liquid in the smaller vessel is:

V1 = π * (D / 2) ^ 2 * H = 2 * D ^ 2 * π cm3.

The volume of liquid poured into a smaller vessel is equal to:

V2 = π * (2 * D / 2) ^ 2 * h = D ^ 2 * h * π cm3.

Since the volume of the liquid did not change during overflow, then V1 = V2.

2 * D ^ 2 * π = D ^ 2 * h * π.

h = 2 cm.

Answer: The liquid level will be at a height of 2 cm.