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A solid pyramid has a unit (1 by 1) square base lying in the x-y plane with vertices at (0,0,0), (0,1,0), (1,1,0) and (1,0,0), and it tapers to a single apex at the point (0,2,2). Every cross-section taken parallel to the x-y plane is a square. Determine the volume of this pyramid.

1. 1/3
2. 2/3
3. 1/2
4. 1

Correct answer: 2/3

Solution

The apex is at z = 2, so the perpendicular height above the base plane is 2; with base area 1, the volume is (1/3)(1)(2) = 2/3.

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