Question

please help its urgent if a polyhedron has 50 edges and 30 vertices find the number of faces it will have

Answer 1

Step-by-step explanation:

it will solve using euler's rule

F+V=E-2

F+30=50-2

F+30=48

F=48-30

F=18

Answer 2

Given:

(i) A polyhedron has 50 edges and 30 vertices.

To find:

(i) The number of faces it will have

Solution:

According to the Euler's rule for polyhedrons, for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

It is represented mathematically as

V − E + F = 2,

where, V is the total number of vertices,

E is the total number of edges,

F is the total number of faces .

According to the question,

V = 30,

E = 50

So, putting them in the equation, we get:

30 - 50 + F = 2

⇒  F - 20 = 2

⇒ F = 20+2 = 22

So, it would have 22 faces.