A solid sphere of diameter 18cm is placed in an empty vertical cylindrical tank of diameter 24cm enough water is poured into the tank to cover the sphere if the sphere is then removed how far does the water fall
the volume of the sphere is 972π cm^3
since the area of the tank's cross-section is 144π cm^2, the height of the water column occupied by the sphere is
972π / 144π = 6.75 cm
Sorry I don't understand, can you explain well
To find out how far the water falls when the sphere is removed from the tank, we need to consider the initial and final states of the system.
First, let's find the volume of the sphere. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius. Since the diameter of the sphere is 18 cm, the radius (r) is half of that, which is 9 cm.
V_sphere = (4/3)π(9)^3
V_sphere ≈ 3053.63 cm³
Next, we need to find the volume of water in the cylindrical tank. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. The radius of the tank is half of its diameter, which is 12 cm.
V_tank = π(12)^2h
V_tank ≈ 144πh cm³
Since the height of the tank is not given, we need to make an assumption that the height of the tank is at least as tall as the sphere, so that when the sphere is completely submerged, the water level reaches the top of the sphere.
Now, we equate the volume of the sphere with the volume of water in the tank:
V_sphere = V_tank
3053.63 = 144πh
h ≈ 6.87 cm
Therefore, when the sphere is removed from the tank, the water level falls approximately 6.87 cm.