. polyhedron shapes


Best Answer

A polyhedron is a 3-dimensional solid made of polygons. It has flat faces, straight edges, and vertices. For example, a cube, prism, or pyramid are polyhedrons. Cones, spheres, and cylinders are non-polyhedrons because their sides are not polygons and that they have curved surfaces. The plural of a polyhedron is also called polyhedra. They are categorized as prisms, pyramids, and platonic solids.

polyhedron

Formula to find diagonal of cube

Sol. Diagonal of a cube formula is √3 x units.

Derivation of Diagonal of a Cube Formula

considering the side of the cube as x, a face diagonal as r, and body diagonal as d

By using the Pythagoras theorem

We get, x2 + r2 = d2

we know that, face diagonal is √2 x

i.e. r = √2

By substituting the value of r in Pythagoras equation we have,

x2 + (√2 x )2 = d2

x2 + 2x2 = d2

3x2 = d2

d = √3x2

d = √3 x

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