MathDB
Neighbourhood of a box

Source:

May 11, 2006
geometry3D geometryprismsphereAMCAIMErectangle

Problem Statement

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+nπ)/p(m + n \pi)/p, where mm, nn, and pp are positive integers, and nn and pp are relatively prime, find m+n+pm + n + p.
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