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.

zhouxia004 Aug 29, 2023

#1**0 **

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.

Guest Aug 29, 2023