A strange polyhedron

Geometry Level pending

A polyhedron has the following vertices:

  • ( 0 , 0 , 0 ) (0,0,0)
  • ( 0 , 1 , 0 ) (0,1,0)
  • ( 1 , 1 , 0 ) (1,1,0)
  • ( 1 , 0 , 0 ) (1,0,0)
  • ( π , e , 1 ) (\pi, e, 1)

What is its volume to 3 decimal places?


The answer is 0.333.

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Apr 8, 2017

For the last point, it doesn't really matter what the x x and y y coordinates are.

It will have the same volume as a pyramid of unit area and height 1 1 , which is:

V = 1 3 ≈ 0.333 V = \frac{1}{3} \approx \boxed{0.333}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Ha ha, didn't know that generalization! I actually used this formula:

Steven Chase - 4 years, 2 months ago

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