## Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D

**Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D**

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### Representing 3-D in 2-D Exercise 19 – Selina Concise Mathematics Class 8 ICSE Solutions

**Question 1.**

If a polyhedron has 8 faces and 8 vertices, find the number of edges in it.

**Solution:**

Faces = 8

Vertices = 8

using Eulers formula,

F + V – E = 2

8 + 8 – E = 2

-E = 2 – 16

E= 14

**Question 2.**

If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.

**Solution:**

Vertices = 10

Faces = 7

Using Eulers formula,

F + V – E = 2

7 + 10 – E = 2

-E = -15

E = 15

**Question 3.**

State, the number of faces, number of vertices and number of edges of:

(i) a pentagonal pyramid

(ii) a hexagonal prism

**Solution:**

**(i)** A pentagonal pyramid

Number of faces = 6

Number of vertices = 6

Number of edges = 10

**(ii)** A hexagonal prism

Number of faces = 8

Number of vertices = 12

Number of edges = 18

**Question 4.**

Verily Euler’s formula for the following three dimensional figures:

**Solution:**

**(i)** Number of vertices = 6

Number of faces = 8

Number of edges = 12

Using Euler formula,

F + V – E = 2

8 + 6 – 12 = 2

2 = 2 Hence proved.

**(ii)** Number of vertices = 9

Number of faces = 8

Number of edges = 15

Using, Euler’s formula,

F + V – E = 2

9 + 8 – 15 = 2

2 = 2 Hence proved.

**(iii)** Number of vertices = 9

Number of faces = 5

Number of edges = 12

Using, Euler’s formula,

F + V – E = 2

9 + 5 – 12 = 2

2 = 2 Hence proved.

**Question 5.**

Can a polyhedron have 8 faces, 26 edges and 16 vertices?

**Solution:**

Number of faces = 8

Number of vertices = 16

Number of edges = 26

Using Euler’s formula

F + V – E

⇒ 8 + 16 – 26 ≠ -2

⇒ -2 ≠ 2

No, a polyhedron cannot have 8 faces, 26 edges and 16 vertices.

**Question 6.**

Can a polyhedron have:

(i) 3 triangles only ?

(ii) 4 triangles only ?

(iii) a square and four triangles ?

**Solution:**

(i) No.

(ii) Yes.

(iii) Yes.

**Question 7.**

Using Euler’s formula, find the values of x, y, z.

**Solution:**

**Question 8.**

What is the least number of planes that can enclose a solid? What is the name of the solid.

**Solution:**

The least number of planes that can enclose a solid is 4.

The name of the solid is Tetrahedron.

**Question 9.**

Is a square prism same as a cube?

**Solution:**

Yes, a square prism is same as a cube.

**Question 10.**

A cubical box is 6 cm x 4 cm x 2 cm. Draw two different nets of it.

**Solution:**

**Question 11.**

Dice are cubes where the sum of the numbers on the opposite faces is 7. Find the missing numbers a, b and c.

**Solution:**

**Question 12.**

Name the polyhedron that can be made by folding each of the following nets:

**Solution:**

(i) Triangular prism. It has 3 rectangles and 2 triangles.

(ii) Triangular prism. It has 3 rectangles and 2 triangles.

(iii) Hexagonal pyramid as it has a hexagonal base and 6 triangles.

**Question 13.**

Draw nets for the following polyhedrons:

**Solution:**

Net of hexagonal prism:

Net of pentagonal pyramid: