Yes, I'm back with a dreadful puzzle for you...
A 6-inch hole is drilled through a sphere. What is the volume of the remaining portion of the sphere?
 the hole is a circular cylinder of empty space whose axis passes through the center of the sphere - just as a drill would make if you aimed the center of the drill at the center of the sphere and made sure you drilled all the way through.
 the length of the hole [6 inches] is the height of the cylinder that forms the inside surface once the hole is drilled. picture the inside surface as viewed from inside the hole and measure the length of that surface in the direction of the axis of the drill.
The hard way involves calculus. The easy way uses logic.
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