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A 4'' x 6'' x 8'' rectangular solid is cut by slicing through the midpoints of three adjacent sides. Find the volume of the shaded piece that is cut off.

 Aug 29, 2023
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Let the original rectangular solid be ABCD, and let the points where the cuts are made be E, F, and G. Then, EFGH is a square with side length 2, and ABCD is divided into 8 congruent smaller cubes. The shaded piece is made up of the four corner cubes, which have a total volume of 4*(1^3)=4​ cubic inches.

 Aug 29, 2023

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