All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Pythagorean Pyramid (Posted on 2004-04-26) Difficulty: 3 of 5
The pictured tetrahedron has four identical rectangular (i.e., right-angled or pythagorean) triangles as faces, with

and p+q=r.

What's its volume, as a function of p, q and r?

See The Solution Submitted by Federico Kereki    
Rating: 4.1250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 12 of 15 |
(In reply to Solution by Victor Zapana)

Going through the posted solution I see the first mistake in the first solution is the assumption that because angle DBA is a right angle, that the two planes meeting there (and all along line BC) are also perpendicular.  This is not the case. It would be the case only if angle CBA were also right, which it is not.  And in fact the angles are such that there is no height at all: it is zero.  Triangle CDB is coplanar with triangle CBA.
  Posted by Charlie on 2004-04-27 09:18:39

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information