[Math4u] Fun Problems

Here's an old problem, one of my favorites that we haven't had in a
couple years:
A man has 12 coins and one is bad. So eleven coins have the same
weight and one has a different weight. The man puts them on a
balance, some coins on each pan. He can make 3 weighings. This is an
old-fashioned balance with 2 pans on opposite ends of an arm. Of
course he must have the same number of coins on each side but he
doesn't need to weigh all the coins each time.
How can he figure out which coin is bad with 3 weighings if he knows
the bad coin is heavy?
Alternately and far more difficult,
How can he figure out which coin is bad with 3 weighings if it is not
known if the coin is heavy or light?

Another problem:
If the volume of a cube is C*r^3
Where
C is a constant
r is the radius
Using simple calculus instead of looking it up in a book, what is the
surface area of the sphere? Show your logic.
Regards,
Brian

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