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The Cut Cube (Posted on 2019-02-13) Difficulty: 3 of 5
A cube on a table has edge length 24. A plane intersects the cube's four vertical edges at points A, B, C, and D such that point A is a vertex of the cube lying on the table. The heights of points B and C from the table floor are 7 and 12, respectively.

Calculate the volume of the portion of the cube that lies underneath the cutting plane.

No Solution Yet Submitted by Danish Ahmed Khan    
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Simple solution Comment 4 of 4 |
The cut goes from the bottom of one leg to a point half-way up the opposite leg.  That this cut is slightly tilted doesn't matter.  Consider just the bottom half of the cube.  The cut splits this box into two congruent parts.

So the portion described is 1/4 of the cube.

V = (24^3)/4=3456

  Posted by Jer on 2019-02-14 12:16:49
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