Representing 3-D in 2-D Test

Result

Representing 3-D in 2-D Test - 1

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Question 1
1 / -0

A polyhedron has 28 edges and its number of faces is two less than the number of its vertices. What is the respective number of its faces and vertices?

A
12 and 14

B
14 and 16

C
9 and 12

D
8 and 13

Solution

Let the number of vertices be V.

∴ Number of faces, F = V – 2

It is given that the numbers of edges of the polyhedron are 28.

We know that, according to Euler’s formula for polyhedron, F + V – E = 2, where F, V and E are the number of faces, vertices and edges of the polyhedron respectively.

∴V – 2 + V – 28 = 2

⇒ 2V – 30 = 2

⇒ 2V = 32

⇒ V = 16

∴ F = V – 2 = 16 – 2 = 14

Thus, the number of faces and vertices of the polyhedron are 14 and 16 respectively.