# I Intermediate Challenge of the Week #1 03/19/2017

1. Mar 3, 2017

### Greg Bernhardt

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2. Mar 3, 2017

RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all mathematicians". Whether the latter is satisfied will be decided on a case-by-case basis.
3) If you have seen the problem before and remember the solution, you cannot participate in the solution to that problem.
4) You are allowed to use google, wolframalpha or any other resource. However, you are not allowed to search the question directly. So if the question was to solve an integral, you are allowed to obtain numerical answers from software, you are allowed to search for useful integration techniques, but you cannot type in the integral in wolframalpha to see its solution.

CHALLENGE:
Beginning with a cube with each side of length 1", drill a 1" diameter hole all the way through in each of the 3 perpendicular directions. Find the remaining volume. (The answer is $V=1+\sqrt{2}-\frac{3}{4} \pi$ (in cubic inches). This problem is one variation of the Steinmetz Solid. )

Last edited by a moderator: Mar 13, 2017