#2             74. A BORING PROBLEM                       
Bert and his son Phil were listening to a program on the radio.

“I bore a hole through the centre of a solid sphere,” said the man on the radio. “The length of the hole when measured turns out to be 6 centimetres. Now you tell me the volume of the sphere remaining.”

“That’s stupid,” said Phil. “He didn’t say what size drill he used.”

“It’s not stupid,” replied the radio rather huffily. “You don’t need the size of the hole.”

“He must mean that the answer is the same for any sized hole,” said Bert. “But it looks like being a complicated calculation.”

“That depends,” answered the radio. “Maybe it’s a one-liner.”

What is the volume remaining?    
HINT 1

If you have some knowledge of calculus and can integrate, it is interesting to try doing this the long way. Take the radius of the sphere to be R, and regard the sphere with hole as a ‘solid of revolution’.
HINT 2

Perhaps there is a smart way of doing this? Assuming that the answer is independent of the size of the hole, perhaps you might try a particular size?
SOLUTION

Assuming the result is independent of the diameter of the hole, reduce this diameter to zero. Thus the hole degenerates to the diameter of a solid sphere of radius 3 cm. The required volume is now the volume of this sphere, that is, (4/3)..33 = 36 cubic centimetres.
EXTENSIONS

This is another one of those puzzles where there seems to be too little information given. Are there other shapes which have this porperty? For example, what if you made a round hole through the centre of a cube? What about a hole of square cross-section? Might there be similar properties for shapes in the plane?