The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.
Given that,
An octahedron is made by connecting the centers of the faces of the right rectangular prism in the illustration below.
We have to find what is the octahedron's volume.
The Greek term "Octahedron," which means "8 faces," is the source of the English word "octahedron." Eight faces, twelve edges, six vertices, and four edges that intersect at each vertex make up an octahedron, a polyhedron. It is one of the five platonic solids with equilateral triangle-shaped faces.
Since two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid. We can compute the volume of one pyramid, then multiply it by two to obtain the volume of an octahedron.
The pyramid's volume is equal to (Base area ×Height)/3.
Since the pyramid's base is square, its base area is equal to a².
Therefore, The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.
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