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Saturday math puzzle V
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Because, apparently, my previous puzzles have been way too easy, I present to you this much more difficult one.
But first, the answer to Last Week's Puzzle: You are presented with 9 identical-appearing lumps of gold. However, only one of the lumps is pure gold (and weighs more); the rest are gold-plated lead. The only thing you have to determine how much any lump weighs is a simple balance scale. How do you determine which lump is the real one with only two weighings?
Answer:Split the nine lumps into three groups and pick two of them to weigh. Either they balance, which means the real lump is in the third group, or one of the piles on the scales will be heavier. In any case, take the group with the real gold in it and pick two lumps from that group. If they balance, the third lump is the real one, otherwise, whichever is heavier is the real lump. Congratulations to Kelley By The Sea for getting the right answer.
This Week's Puzzle: You work for a manufacturing company and have been asked to produce a particular component. You are to take a copper 
sphere and drill a perfectly cylindrical hole through it such that the hole is exactly 1 inch long (a picture of the cross-section of such a thing is at right). You need to find the amount of copper you need to create each component (because you can take the drilled out copper and reuse it, we only need the volume of the remaining object). Unfortunately, the company that ordered the component forgot to include the desired radius of the sphere. So how much copper will you need?
Post your answer to the comments!
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