In our day to day life, we come across various objects with different shapes and sizes like triangles, squares, circles, etc. Some of these shapes which have length, breadth and height are called 3D or three-dimensional objects. Other objects like a sheet of paper which have a length and breadth are called two-dimensional or 2D shapes. Chapter 19 Representing 3D in 2D explains about how three-dimensional objects can be represented into 2-dimensional objects along with suitable examples related to the concept.

The ICSE Class 8 Maths Selina Solutions Chapter 19 Representing 3D in 2D are very helpful for students from the exam point of view. Here we have provided the solutions prepared by our subject experts of all the questions mentioned in this chapter. These Selina Solutions are solved in a step by step manner for better understanding so that students can refer to these solutions while solving the questions.

## Download ICSE Class 8 Maths Selina Solutions Chapter 19 Representing 3D in 2D

ICSE Class 8 Maths Selina Solutions Chapter 19 Representing 3D in 2D consists of 15 questions and detailed solution of all questions is provided below.

### CHAPTER 19 â€“ REPRESENTING 3-D IN 2-D

**Question 1.Â **

If a polyhedron hasÂ 8Â faces andÂ 8Â vertices, find the number of edges in it.

**Solution:-**

FacesÂ =8

VerticesÂ =8

Using Eulerâ€™s formula,

F+V-E=2

8+8-E=2

-E=2-16

E=14

** QuestionÂ 2.Â **

If a polyhedron hasÂ 10Â vertices andÂ 7Â faces, find the number of edges in it.

**Solution:-**

VerticesÂ =10

FacesÂ =7

Using Eulerâ€™s formula

F+V-E=2

7+10-E=2

-E=-15

E=15

**Question 3.Â **

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

(i) a pentagonal pyramid

**Solution:-**

Â (i) A pentagonal pyramid

Number of facesÂ =6

Number of verticesÂ =6

Number of edgesÂ =10

(ii) A hexagonal prism

**Solution:-**

(ii) A hexagonal prism

Number of faces =Â 8

Number of verticesÂ =12

Number of edgesÂ =18

**QuestionÂ 4**.

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

**Â Solution:**

(i) Number of vertices = 6

Number of facesÂ =8

Number of edgesÂ =12

Using Euler formula

F+V-E=2

F+V-12=2

2=2Â hence proved.

**Solution**:

(ii) Number of verticesÂ =9

Number of facesÂ =8

Number of edgesÂ =15

Using, Euler’s formula,

F+V-E=2

9+8-15=2

2=2

Hence proved.

**Solution:-**

(iii) Number of verticesÂ =9

Number of facesÂ =5

Number of edgesÂ =12

Using, Euler’s formula,

F+V-E=2

9+5-12=2

2=2Â hence proved.

**QuestionÂ 5.**

Can a polyhedron haveÂ 8Â faces,Â 26Â edges andÂ 16Â vertices?

**Solution:-**

Number of facesÂ =8

Number of verticesÂ =16

Number of edgesÂ =26

Using Euler’s formula

F+V-E

8+16-26â‰ -2

8+16-26â‰ -2

-2â‰ 2

No, a polyhedron cannot haveÂ 8Â faces,Â 26Â edges andÂ 16Â vertices.

**Question 6.Â **

Can a polyhedron have?

(i)Â 3Â triangles only?

**Solution:-**

(i) No.

(ii)Â 4Â triangles only?

**Solution:-**

(ii) Yes.

(iii) A square and four triangles?

**Solution:-**

(iii) Yes.

**QuestionÂ 7.Â **

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

Faces | Vertices | Edges | |

(i) | x | 15 | 20 |

(ii) | 6 | Y | 8 |

(iii) | 14 | 26 | z |

**Solution:-**

(i)F+V-E=2

x+15-20=2

x-5=2â‡’x=2+5=7

(ii)F+V-E=2

15+y-26=2

y-11=2

y=2+11â‡’y=13

(iii)Â F+V-E=2

14+26-Z=2

-Z=2-40â‡’Z=38

**Question 8.Â **

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

**Solution:-**

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

The name of the solid is Tetrahedron.

**Question 9.Â **

Is a square prism same as a cube?

**Solution:Â **

Yes, a square prism is same as a cube.

**QuestionÂ 10.Â **

AÂ cubicalÂ boxÂ is \(6 \mathrm{cm} \times 4 \mathrm{cm} \times 2 \mathrm{cm}\)Â .Â DrawÂ twoÂ differentÂ netsÂ ofÂ it.

**Solution: **

**Â Question 11.Â **

Dice are cubes where the sum of the numbers on the opposite faces isÂ 7.Â Find the missing numbers a, bÂ and c.

**Solution:-**

**QuestionÂ 12.Â **

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

(i)

**Solution:-**

(i)Â TriangularÂ prism.Â ItÂ hasÂ 3Â rectanglesÂ andÂ 2Â triangles.

**(ii)**

**Solution:-**

(ii)Â TriangularÂ prism.Â ItÂ hasÂ 3Â rectanglesÂ andÂ 2Â triangles.

(iii)

**Solution:-**

(iii)Â HexagonalÂ pyramidÂ asÂ itÂ hasÂ aÂ hexagonalÂ baseÂ andÂ 6Â triangles.

**QuestionÂ 13.**

DrawÂ netsÂ forÂ theÂ followingÂ polyhedrons:

**Solution:-**

NetÂ ofÂ hexagonalÂ prism:

Net of pentagonal pyramid:

### ICSE Class 8 Maths Selina Solutions Chapter 19 – Representing 3D in 2D

In chapter 19 Representing 3D in 2D students will learn Eulerâ€™s formula, two-dimensional shapes, three-dimensional shapes, view of 3D shapes, etc. The concepts covered in the chapter gives a basic introduction so that students have some knowledge about it before they step into the next class. The chapters define each and every topic in a simple and understandable manner so that students donâ€™t get confused while going through the chapter.

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