Question

Derive a volume formula for truncated octahedron. Show steps.

Answer 1

The solid can be formed from an Octahedron via Truncation by removing six Square Pyramids, each with edge slant height and height , where is the side length of the original Octahedron. From the above diagram, the height and base area of the Square Pyramid are

			(1)
			(2)

The Volume of the truncated octahedron is then given by the Volume of the Octahedron

(3)

minus six times the volume of the Square Pyramid,

(4)