Question

A solid has 40 faces and 60 edges. How many vertices does it have?

Answer 1

faces+vertices - edges = 2
there fore vertices equal to 22

Answer 2

The solid has 22 vertices

Given :

A solid has 40 faces and 60 edges

To find :

The number of vertices of the solid

Concept :

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges

Solution :

Step 1 of 2 :

Write down number of faces , number of vertices , number of edges

F = Number of faces = 40

E = Number of edges = 60

V = Number of vertices = ?

Step 2 of 2 :

Find number of vertices

We use Euler’s formula

By Euler’s formula

F + V = E + 2

⇒ 40 + V = 60 + 2

⇒ V + 40 = 62

⇒ V = 62 - 40

⇒ V = 22

The solid has 22 vertices

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