# NCERT Solutions Class 8 Maths Chapter 10

## NCERT Solutions for Class 8 Mathematics Chapter 10 – Visualising Solid Shapes

Mathematics is necessary in daily life. It promotes logical and critical thinking skills among students in school. It provides opportunities for developing important intellectual skills in problem-solving, reasoning, and so on.. It demands a lot of practice while trying to enhance students’ intellectual development. However, If students find it difficult to answer tough mathematical examples, exercises or questions, they can refer to the study material provided by Extramarks which will ensure clarity of each concept and each exercise in an easy and step-by-step manner to encourage a smooth and deeper understanding among students.   . In fact everything a student needs to learn and grow in Mathematics is included in NCERT Solutions for Class 8 Mathematics Chapter 10.

Visualizing Solid Shapes is important as it involves three-dimensional objects, properties, formulas, and calculations. The chapter covers topics related to the basic configuration of two-dimensional and three-dimensional objects. Our NCERT Solutions for Class 8 Maths Chapter 10 are based on the 2022-2023 CBSE syllabus and will provide students with solved questions given in the NCERT textbook that they would require to get the best score in the examinations.

Extramarks, an online learning platform, aims to make learning Mathematics engaging and fun. It encourages them to think rationally and solve problems. The NCERT Solutions for Class 8 Mathematics Chapter 10  assist students in their exam preparation by allowing them to practice essential questions given in the NCERT textbook. Students can also use the Extramarks web portal and mobile app to access practice tests, mock tests, CBSE books, and other resources. It will ensure that even the minutest doubt is resolved and the students develop an interest in learning and mastering the topic with ease.

## Key topics covered in Visualising Solid Shapes Class 8 Mathematics Chapter 10

NCERT Solutions for Class 8 Mathematics Chapter 10 provided on the Extramarks website is an excellent resource for students who want to study more effectively and get excellent grades in their exams. It will provide students with comprehensive answers to the chapter containing thorough information about each topic and each exercise covered in the chapter, allowing students to prepare effectively before the exams. In other words, the effort has been made to ensure that nothing is left in the process.

The main topics covered in Class 8 Mathematics Chapter 10 are as follows:

• Introduction
• Views of 3D-shapes
• Mapping Space around Us
•  Faces, Edges, and Vertices

### Introduction

The chapter Visualising Solid Shapes of Class 8 is part of the geometry section of Mathematics and it covers the basics of Geometry required in higher classes. The students learn to identify vertices, faces and edges of 2D and 3D objects. It also helps them know the area and volume of various solid figures. Hence, students must go through this chapter thoroughly.

You can find the entire chapter covered in detail with their solutions in the NCERT Solutions for Class 8 Mathematics Chapter 10 available on the Extramarks official website. To enjoy the maximum benefit of these resources, students just need to register themselves at Extramarks official website and stay ahead of the pack.

### Views of 3D shapes

A 3D shape looks different from the different positions and angles. Based on it, different perspectives can be drawn.

For example, the front view of the hut is different from its back view, and the side view is not the same as the top view.

Similarly, the views from different positions would be different for a glass.

You can also see different views by joining the cubes.

To know more about the views of 3D shapes, you can refer to the NCERT solutions for Class 8 Mathematics Chapter 10 available on the Extramarks website.

### Mapping Space around Us

A map depicts the location of one thing in relation to others.

Some important points related to the map:

1. Various symbols are used to locate various objects or locations on the map.
2. It shows that the location of an object will remain constant regardless of the observer’s point of view.
3. When drawing a map, a specific scale is used to ensure that the lengths drawn are proportional to the distance between the source figures.

### Faces, Edges, and Vertex

• Faces – The faces are all the flat surfaces of the 3D objects. They meet at the line segments..
• Edges – Edges are the line segments that make up the structure of solid forms. The two faces meet at the 3D shapes’ edges.
• Vertex – The vertex is the corner point of a solid shape. The vertex is where the two edges meet. Vertices are plural of the vertex.
• Polyhedron – The solids made up of polygonal regions, i.e. faces and edges, is called a Polyhedron.
• Convex Polyhedron – The diagonals that lie in the interior of the polygon are called a Convex Polyhedron.
• Regular Polyhedron – A polyhedron is said to be regular if its faces are made up of regular polygons, and the same number of faces meet at each vertex.
• Prism – A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e. lateral faces, are parallelograms in space.
• Pyramid- A pyramid is a polyhedron whose base is a polygon (of any number of sides) and whose lateral faces are triangles with a common vertex.

There are different types of pyramids. Some of them are listed below.

• Triangular pyramid: A triangular pyramid is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
• Hexagonal pyramid: A hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point.
• Square pyramid: A square pyramid is a pyramid having a square base.
• Rectangular pyramid: If the base of a pyramid is rectangular, then it is called a rectangular pyramid.
• Euler’s formula – It depicts the relationship between a polyhedron’s edges, faces, and vertices. Every polyhedron will meet the F + V – E = 2 conditions,

Where F is the number of polyhedron faces, V is the number of polyhedron vertices, and E is the number of polyhedron edges.

Many students find it difficult to visualize and comprehend the different forms of solids. Extramarks NCERT Solutions for Class 8 Mathematics Chapter 10 provides multiple visual demonstrations of real-life examples for students to better understand the various solid forms covered above.

## NCERT Solutions for Class 8 Mathematics Chapter 10 Exercises &  Solutions

Extramarks is one of the best online learning platforms for students preparing for Mathematics. Our study materials have various tools and tips to quickly revise formulas, and properties, which will help students to solve the problems quickly and easily.

NCERT Solutions for Class 8 Mathematics Chapter 10 include various questions for students to practice. The detailed and well-structured answers help students to get in-depth knowledge of the chapter visualizing solid shapes and, thus, develop interest to find answers and encourage them to solve more challenging questions and be confident. Students will learn the rules of visualizing solid shapes of different forms to think rationally and solve problems on their own. NCERT Solutions for Class 8 Mathematics Chapter 10  are simple to comprehend for students who desire to ace their examinations. It includes solutions to all exercise questions, miscellaneous problems as well as some extra CBSE questions. Students are recommended to solve the CBSE sample papers for further practice.

 Chapter 10 – Visualizing Solid Shapes Exercises Exercise 10.1 Views of 3D-Shapes 4 Question and Answer Solutions Exercise 10.2 Mapping Space Around Us 4 Question and Answer Solutions Exercise 10.3 Faces, Edges and Vertices 8 Questions & Solutions

Students can enjoy a seamless and wholesome learning experience by choosing Extramarks.  NCERT Solutions for Class 8 Mathematics Chapter 10 is written in very easy language. It has been prepared after extensive research and following CBSE Syllabus and  CBSE past years’ question papers. Extramarks leaves no stone unturned while giving  the best learning material to students while combining fun and  learning activities through its own repository of study materials to enhance their learning experience

Extramarks platform has study solutions for all grades and subjects. Refer to the  links below to get access to our NCERT Solutions study materials:

## NCERT Exemplar Class 8 Mathematics Chapter 10

Extramarks help students by providing the best study tools, such as NCERT Solutions for Class 8 Mathematics Chapter 10. These assist pupils in performing well on their board exams. Extramarks  NCERT Solutions for Class 8 Mathematics Chapter 10 provide students with unlimited practice questions, thorough concepts, and stepwise derivations to help them understand numerous topics related to Visualising Solid Shapes.

NCERT Exemplar’s book consists of different questions with varying levels of difficulty from easy to advanced levels for thorough and complete preparation. . It helps students develop more interest to solve challenging questions in mathematics and get more significant insights into the chapter. It helps develop confidence during their preparation as they have solved questions from basic to advanced levels to improve their preparation and help them get 100% scores in their exams.

The NCERT Exemplar presents various tips, hints, and tactics for efficiently solving problems without making silly mistakes. Students can study more efficiently and enjoy their learning pattern with the help of academic notes such as NCERT Exemplar and Extramarks  NCERT Solutions for Class 8 Mathematics Chapter 10

## Key Features Of NCERT Solutions for Class 8 Mathematics Chapter 10

To obtain a good score in exams, revision of previous concepts is a must. Hence, NCERT Solutions for Class 8 Mathematics Chapter 10 offers a complete solution for all problems provided on Extramarks’ website.

Extramarks’ study material has the following main features:

• Extramarks NCERT Solutions for Class 8 Mathematics Chapter 10 are written by subject matter experts with years of experience in the subject.
• Includes all concepts from the CBSE syllabus and is based on the most recent NCERT 2022-23 pattern. Students will get detailed and authentic solutions without having to look anywhere else.
• The answers present extensive and pertinent information clearly and in an easy-to-understand manner. .
• It assists students in reinforcing their fundamentals, making it easier for them to comprehend more complicated themes.
• Time management, problem-solving, and analytical skills can all be developed by students.

Q.1 For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The first one is done for you.

Ans

Q.2 For each of the given solid, the three views are given. Identify for each solid the corresponding top,

front and side views.

Ans

Q.3 For each given solid, identify the top view, front view and side view.

Ans

Q.4 Draw the front view, side view and top view of the given objects.

Ans

Q.5 Look at the given map of a city.

1. Colour the map as follows: Blue-water, red-fire station, orange-library, yellow – schools, Green – park, Pink – College, Purple – Hospital, Brown – Cemetery.
2. Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.
3. In red, draw a short street route from Library to the bus depot.
4. Which is further east, the city park or the market?
5. Which is further south, the primary school or the Sr. Secondary School?

Ans

1. Between the Market and the City Park, the City Park is further east.
2. Between the Primary School and the Sr. Secondary School, the Sr. Secondary School is further south.

Q.6 Draw a map of your class room using proper scale and symbols for different objects.

Ans

Q.7 Draw a map of your school compound using proper scale and symbols for various features like play ground main building, garden etc.

Ans

Q.8 Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

Ans

Q.9 Can a polyhedron have for its faces

(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?

Ans

(i) No, such a polyhedron is not possible. A polyhedron has minimum 4 faces.

(ii) Yes, a triangular pyramid has 4 triangular faces.

(iii) Yes, a square pyramid has a square face and 4 triangular faces.

Q.10 Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).

Ans

Yes, it is possible, if a polyhedron has minimum of 4 faces

Q.11 Which are prisms among the following?

Ans

(i) It is not a polyhedron as it has a curved surface. Therefore, it will not be a prism also.

(ii) It is a prism.

(iii)Since the faces are triangular, so it is a pyramid. Hence, it is not a prism

(iv) It is a prism.

Q.12 (i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

Ans

(i) A prism that has a circle as its base can be thought of as a circular prism.

(ii) A pyramid that has a circle as its base can be thought of as a circular pyramid.

Q.13 Is a square prism same as a cube? Explain.

Ans

A square prism has a square as its base. Its height is not necessarily same as the side of the square. Thus, it is not necessary that always a square prism is same as a cube. It can be cuboid also.

Q.14 Verify Euler’s formula for these solids.

Ans

The Euler’s formula F+V–E = 2

(i) Number of faces = F = 7

Number of vertices = V = 10

Number of edges = E = 15

We have, F + V − E = 7 + 10 − 15

= 17 − 15

= 2

Hence, verified.

(ii) Number of faces = F = 9

Number of vertices = V = 9

Number of edges = E = 16

F + V − E = 9 + 9 − 16

= 18 − 16

= 2

Hence, verified.

Q.15 Using Euler’s formula find the unknown.

 Faces ? 5 20 Vertices 6 ? 12 Edges 12 9 ?

Ans

By Euler’s formula, we have F + V − E = 2

(i) F + 6 − 12 = 2

F − 6 = 2

F = 8

(ii) 5 + V − 9 = 2

V − 4 = 2

V = 6

(iii) 20 + 12 − E = 2

32 − E = 2

E = 30

Thus, the table can be completed as:

 Faces 8 5 20 Vertices 6 6 12 Edges 12 9 30

Q.16 Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Ans

Number of faces = F = 10

Number of edges = E = 20

Number of vertices = V = 15

By using Euler’s Formula, we can find whether a polyhedron satisfies the given conditions.

Therefore, we have, F + V − E = 2

But, F + V − E = 10 + 15 – 20

= 25 – 20

= 5 ≠ 2

Since Euler’s formula is not satisfied, such a polyhedron is not possible.