A cylindrical vessel with a base radius of 50 cm is half-filled with water. A metal ball with a radius of 30 cm

A cylindrical vessel with a base radius of 50 cm is half-filled with water. A metal ball with a radius of 30 cm was thrown into the vessel, which was completely submerged in the water. How many centimeters did the water level in the vessel rise?

As you know, the volume of the ball is equal to:

V = 4/3 * π * r³.

Since r = 30 cm, the volume of this ball is equal to:

V = 4/3 * π * 30³,

V = 4/3 * π * 27000,

V = 36000 * π.

As a result of the ball hitting the cylinder, the water level in it rose by h cm, that is, an additional water cylinder was formed, the volume of which is equal to the volume of the ball:

π * r² * h = 36000 * π,

r² * h = 36000.

Since r = 50 cm, we get:

2500 * h = 36000,

h = 36000: 2500,

h = 14.4 cm.

Answer: 14.4 cm.