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

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 – REPRESENTING 3-D IN 2-D

Question 1. 

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

Solution:-

Faces =8

Vertices =8

Using Euler’s 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 Euler’s 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

Solution:-

 (i) A pentagonal pyramid

Number of faces =6

Number of vertices =6

Number of edges =10

(ii) A hexagonal prism

Solution:-

(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:

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-1

 Solution:

(i) Number of vertices = 6

Number of faces =8

Number of edges =12

Using Euler formula

F+V-E=2

F+V-12=2

2=2 hence proved.

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-2

Solution:

(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.

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-3

Solution:-

(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

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?

Solution:-

(i) No.

(ii) 4 triangles only?

Solution:-

(ii) Yes.

(iii) A square and four triangles?

Solution:-

(iii) Yes.

Question 7. 

Using Euler’s formula, find the values of 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=2⇒x=2+5=7

(ii)F+V-E=2

15+y-26=2

y-11=2

y=2+11⇒y=13

(iii) F+V-E=2

14+26-Z=2

-Z=2-40⇒Z=38

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 \(6 \mathrm{cm} \times 4 \mathrm{cm} \times 2 \mathrm{cm}\) . Draw two different nets of it.

Solution:

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-4

 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.

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-5

Solution:-

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-6

Question 12. 

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

(i)

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-6

Solution:-

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

(ii)

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-7

Solution:-

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

(iii)

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-8

Solution:-

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

Question 13.

Draw nets for the following polyhedrons:

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-9

Solution:-

Net of hexagonal prism:

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-10

Net of pentagonal pyramid:

Class 8 Maths Selina Solutions for Chapter 19 Representing 3D in 2D-11

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

In chapter 19 Representing 3D in 2D students will learn Euler’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 don’t get confused while going through the chapter.

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