Three Pyramids in a CubeDate: 03/04/2002 at 01:23:22 From: Chaitu Subject: Pyramids and prisms Hi, I want to know how 3 pyramids can fit exactly into a rectangular prism. My teacher said it was possible, but i can't figure it out. Date: 03/04/2002 at 09:19:12 From: Doctor Rick Subject: Re: Pyramids and prisms Hi, Chaitu. They won't be symmetrical pyramids: their peaks won't be above the middle of the base, but above one corner of the base. Here is a cube: _________________________ | \ | \ | \ | \ | \ | \ | \_____________|___________\ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |___________|_____________| | \ | \ | \ | \ | \ | \ | \|________________________\| Imagine that the lower right square is the front face of the cube, and the parallelogram on the left is the left face of the cube. Now I add a "body diagonal from one corner to the opposite corner, and two "face diagonals" from the same top corner to the opposite corners on the back and right faces of the cube: _________________________ | \ /| \ | \ // |\ \ | \ / | \ \ | \______/___/__|___________\ | | / / | \ | | | / | \ | | |/ / | | | /| / | \ | | / | | \ | | / | / | | | / | / | \ | | / | / | | |/__________|_____________| \ | \ | \ \ | \ | / \ | \ | / \ \ | \|________________________\| You can see one square pyramid: its base is the bottom face of the cube, and its peak is the top back right corner, where the diagonals meet. Now if you add one more face diagonal, you will have all the edges of all three pyramids that fit together to make the cube. Can you see where to add the face diagonal, and where the bases of the other two pyramids are? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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