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# Cube Problem

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A rectangular prism has dimensions of 4 by 4 by 5. The cube is painted on all faces. Then the block is cut into eighty 1 by 1 by 1 cubes. How many of these cubes have no paint on any face?

Guest Jun 13, 2017
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#1
+5552
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the volume of the prism = 4 * 4 * 5 = 80 cubic units

Imagine a shell that surrounds the prism that has a thickness of 1 cubic unit. All of the cubes in this shell have paint on them. All of the cubes inside the shell have no paint on them.

the volume of the prism inside the shell = (4 - 2) * (4 - 2) * (5 - 2) = 2 * 2 * 3 = 12 cubic units

So...there are 12 cubes without any paint on them.

hectictar  Jun 13, 2017
#2
+79784
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Looking at the 4 x 4  face, we have  4 x (5 - 2) = 4 x  3  = 12   "inner cubes"  that will have no paint on them

CPhill  Jun 13, 2017
edited by CPhill  Jun 13, 2017

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