Question

what will be the number of vertices in a polyhedron which has 33 edges and 15 faces

Answer 1

                           ======================

♦ Polyhedron is a 3-D object .

♦ The Euler's Formula establish a relationship between Face, Vertices and Edges of any 3 - D object.

Given,

Edges = 33

Faces = 15.

Vertices = ?

Using Euler's Formula,

⇒ Face + Vertices - Edge = 2

⇒ 15 + Vertices - 33 = 2

⇒ Vertices - 18 = 2

⇒ Vertices = 2 + 18

∴ Vertices = 20.

The polyhedron has 20 vertices.

Hope it helps !!