Question

Prove Euler’s formula for the model of cube and cuboid.​

Answer 1

Step-by-step explanation:

By Euler's formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula F + V = E + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges.

V - E + F = 2; or, in words: the number of vertices, minus the number of edges, plus the number of faces, is equal to two. ... V - E + F = 12 - 30 + 20 = 32 - 30 = 2, as we expected. Euler's formula is true for the cube