. polyhedron shapes
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.
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