Imagine a sphere with a hole that has been drilled clean through its center (i.e. a cylindrical piece of the sphere is now missing). This new shape, with the core missing, has height of 6 when standing on the ground (i.e. flat side on the ground). What is the volume of this shape?
This is a popular problem commonly referred to as the Napkin ring problem.
Essentially, irrespective of the diameter of the drilled cylinder, the volume of the resultant object will always be equal to the volume of a sphere whose diameter is the same length as the height of the object. In this case, the volume of the sphere is $4/3\pi (6/2)^3$ or roughly 113.1 cubic units, no matter what the diameter of the original sphere was. As long as it was drilled out perfectly till the height of the new object is 6, the volume remains the same.