Suppose a ball is completely submerged inside a cylinder filled with water displacing some of the water in the cylinder. Assume the ball and the cylinder both have a diameter of 10 centimeters, and the diameter of the ball is the same as the height of the cylinder. Determine the volume of water that can remain in the cylinder after the ball is inserted so that the water rises to the top edge of the cylinder without spilling

Accepted Solution

In terms of radius, the volume of the cylinder is
.. Vc = πr²×(2r) = 2πr³

In terms of radius, the volume of the sphere is
.. Vs = (4/3)πr³

Then the volume of water is the difference
.. Vw = Vc -Vs
.. = (2 -4/3)πr³
.. = (2/3)πr³
For the given dimensions, this is
.. Vw = (2π/3)*(5 cm)³
.. = 250π/3 cm³
.. ≈ 261.8 cm³ . . . . . . . . volume of water in the cylinder