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'Impossible' Solid's Volume (Posted on 2006-11-04) Difficulty: 4 of 5
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A solid whose plan view and front and side elevations resembled a multiplication symbol (x) bounded by a circle may be viewed here.

It is the third on that page.

The object can be created by imposing 3 cylinders on a cube in each of the x, y and z dimensions.

If the edges of the cube are of unit length, What is the volume of this object?

How mundane (as being simple) a solution can we get?

See The Solution Submitted by brianjn    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Starting... | Comment 2 of 11 |
(In reply to Starting... by Larry)

(3) Some of the material of the cube would be removed by any of the 3 cylindar cuts (such at the bits near the corners); some by 2 of the cylindars, and some by only one cylindar.  That which remains is the volume we seek, of course.

(4) The first cut decreases the volume from 1 to
   Pi/4 = 0.785398163397

  Posted by Larry on 2006-11-04 14:51:55

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