Visualising Solid Shapes Test

Result

Visualising Solid Shapes Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

A polyhedron has 15 faces and the number of its edges is 1 more than twice the number of its vertices. What is the number of its vertices?

A
12

B
14

C
16

D
18

Solution

By Euler’s formula, we know that for a polyhedron,

F + V − E = 2 where F, V and E are the number of faces, vertices and edges of the polyhedron.

Now, F = 15, E = 2V + 1

∴ 15 + V − (2V + 1) = 2

⇒ 15 + V − 2V − 1 = 2

⇒ 14 − V = 2

⇒ V = 14 − 2 = 12

Thus, the required polyhedron has 12 vertices.

Hence, the correct answer is option A.
Question 2
1 / -0

A polyhedron has 14 faces and 24 vertices. What is the number of edges of the polyhedron?

A
28

B
32

C
36

D
42

Solution

By Euler’s formula, we know that for a polyhedron,

F + V − E = 2, where F, V, and E are the number of faces, vertices, and edges of the polyhedron.

Now, F = 14 and V = 24

∴ 14 + 24 − E = 2

⇒ E = 38 − 2 = 36

Thus, the required polyhedron has 36 edges.

The correct answer is C.