Difference between revisions of "2003 AIME I Problems/Problem 5"

 
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== Problem ==
 
== Problem ==
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Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures 3 by 4 by 5 units. Given that the volume of this set is <math> (m + n \pi)/p, </math> where <math> m, n, </math> and <math> p </math> are positive integers, and <math> n </math> and <math> p </math> are relatively prime, find <math> m + n + p. </math>
  
 
== Solution ==
 
== Solution ==

Revision as of 19:07, 6 August 2006

Problem

Consider the set of points that are inside or within one unit of a rectangular parallelepiped (box) that measures 3 by 4 by 5 units. Given that the volume of this set is $(m + n \pi)/p,$ where $m, n,$ and $p$ are positive integers, and $n$ and $p$ are relatively prime, find $m + n + p.$

Solution

See also