In a cylindrical vessel, the liquid level reaches 12 cm.

In a cylindrical vessel, the liquid level reaches 12 cm. At what height will the liquid level be if it is poured into a second vessel, the diameter of which is 4 times the first.

To solve the problem, let’s compare the volumes of two vessels in order to find out how the change in the diameters of these vessels will affect them:
V = S * H, where V is the volume of the vessel, S is the cross-sectional area, H is the height of the liquid level.
Since the volume of the liquid is the same, and knowing that the diameter of the vessel has increased by 4 times, we can find the height of the level of the second vessel:
3.14 * d² * 12/4 = 3.14 * 16d² * H / 4;
3 = 4H;
H = 3/4 cm.
Answer: in the second vessel, the liquid level will be at a height of 3/4 centimeter.