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point distance of 1 from rectangular prism, find volume

Source: Putnam 1984 A1

August 31, 2021
geometry3D geometryprism

Problem Statement

Let AA be a solid a×b×ca\times b\times c rectangular brick, where a,b,c>0a,b,c>0. Let BB be the set of all points which are a distance of at most one from some point of AA. Express the volume of BB as a polynomial in a,b,a,b, and cc.
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