NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

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# NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

Edited By Ramraj Saini | Updated on Oct 09, 2023 05:37 PM IST

## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

Visualizing Solid Shapes Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at Craeers360 keeping in mind of the latest syllabus and pattern of CBSE 2023-23. In this NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes you will study solid objects like cubes, cuboids, cones, spheres, hemispheres, etc. You must have noticed that 3-dimensional objects look different when you look from different positions or different angles. To simplify its study there are defined viewpoints (front view, side view, top view) for the 3D object.

In NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes, maximum questions are related to finding front view, side view, and top view of the 3D geometry. Important topics like views of 3D shapes, mapping space around us, faces, edges, and vertices of the objects are covered in this chapter. NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes are very helpful in engineering drawing, locating the place and will build a basic understanding of the 3D shapes. Here you will get the detailed NCERT Solutions for Class 8 Maths by clicking on the link.

## Visualizing Solid Shapes Class 8 Solutions - Important Formulae

• Polyhedron: A solid object bordered by polygons (platonic solid).

• Euler's Formula: For a polyhedron with F faces, V vertices, and E edges:

F + V - E = 2

• Prism: A solid with parallelogram side faces and congruent parallel polygon ends (bases). A prism consists of two triangular faces, three rectangular faces, six vertices, and nine edges.

• Pyramid: A polyhedron with a polygonal base and additional triangular faces converging at a common vertex. A pyramid typically consists of one square face, four triangular faces, five vertices, and eight edges.

• Tetrahedron: A type of triangular pyramid where the base is a triangle.

• Dimensions of a Solid: Three-dimensional objects have three measurements (length, width, and height), while two-dimensional objects have two measurements (length and breadth or depth).

• Mapping: Maps are different from photographs, as they show the relationships between objects and locations using symbols and a set scale.

• Faces, Vertices, and Edges: In a polyhedron, faces are polygonal sections, edges are line segments connecting faces, and vertices are the points where edges intersect.

Free download NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes for CBSE Exam.

## Visualizing Solid Shapes Class 8 NCERT Solutions (Intext Questions and Exercise)

Visualizing solid shapes class 8 NCERT solutions - Topic 10.1 Introduction

Matched items are:

## (i) An agricultural field

Two rectangular cross paths inside a rectangular park.

(ii) A groove

A circular path around a circular ground.

(iii) A toy

A triangular field adjoining a square field.

(iv) A circular park

A cone has been taken out of a cylinder.

(v) A cross path

A hemisphere surmounted on a cone.

Matched objects are:

Class 8 maths chapter 10 question answer - exercise: 10.1

Object Side view Top view

Matched objects are:

(1) →iii)→iv)

(2) →i) →v)

(3) →iv)→ii)

(4) →v) →iii)

(5) →ii) →i)

(a) Different views have given: (i) Front, (ii) Side, (iii) Top.

(b) (i) Side view, (ii) Front view, (iii) Top view.

(c) (i) Front view, (ii) Side view, and (iii) Top view.

(d) (i) Front view, (ii) Side view, and (iii) Top view.

(a) (i) Top view, (ii) Front/ Side view, and (iii) Side/ Front view.

(b) (i) Side view, (ii) Front view, and (iii) Top view.

(c) (i) Top view, (ii) Side view, and (iii) Front view.

(d) (i) Side view, (ii) Front view, and (iii) Top view.

(e) (i) Front view, (ii) Top view, and (iii) Side view.

A military tent

The front view, top view, and side view of a tent are shown below:

The front view, top view, and side view of a tent are shown below:

A table

The front view, top view, and Side view of the table are shown below:

A nut

The front, top, and side views of the nut are:

A hexagonal block

The front view, side view and top view of the hexagonal block are shown below:

The front view, side view and top view of the dice as shown below:

A solid

The front view, side view and top view of the given solid.

Class 8 maths chapter 10 ncert solutions - exercise: 10.2

Question:1(a) Look at the given map of a city.

Colour the map as follows: Blue-water, red-fire station, orange-library, yellow
schools, Green - park, Pink - College, Purple - Hospital, Brown - Cemetery.

(a) Coloured map shown:

Question:1(b) Look at the given map of a city.

Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.

(b) marked points of intersections "X" and "Y":

Question:1(c) Look at the given map of a city.

In red, draw a short street route from Library to the bus depot.

Route from Library to bus depot is shown:

Question:1(d) Look at the given map of a city.

Which is further east, the city park or the market?

(d) The city park is further east.

Question:1(e) Look at the given map of a city.

Which is further south, the primary school or the Sr. Secondary School?

(e) Sr. Secondary School is further south.

Do it yourself.

Do it with your own imagination.

Do it with your own imagination.

NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes - Topic 10.4 Faces, Edges and Vertices

Solid

F

V

E

F+V

E+2

Cuboid

Triangular pyramid

Triangular prism

Pyramid with square base

Prism with square base

 Solid F V E F+V E+2 Cuboid 6 8 12 14 14 Triangular pyramid 4 4 6 8 8 Triangular prism 5 6 9 11 11 Pyramid with square base 5 5 8 10 10 Prism with square base 6 8 12 14 14

Class 8 visualizing solid shapes ncert solutions - exercise: 10.3

Question:1(i) Can a polyhedron have for its faces

3 triangles?

(i) No, a polyhedron cannot have 3 triangles for its faces .

Question:1(ii) Can a polyhedron have for its faces

4 triangles?

(ii) Yes, a polyhedron having 4 triangles is pyramid on triangular base.

Question:1(iii) Can a polyhedron have for its faces

a square and four triangles?

(iii) Yes, a polyhedron can have faces of a square and four triangles which makes a pyramid on square base.

Yes , it is possible if the number of faces is four or more than four.

Question:3(i) Which are prisms among the following?

(i) a nail is not a prism.

Question:3(ii) Which are prisms among the following?

(ii) The unsharpened pencil is a prism.

Question:3(iii) Which are prisms among the following?

(iii) Table weight is not a prism.

Question:3(iv) Which are prisms among the following?

(iv) Given box is a prism.

Question:4(i) How are prisms and cylinders alike?

(i) A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., lateral faces are parallelograms in shape. Also, the cylinder has base on top and bottom and faces are parallel.

No , not always, because it can be a cuboid also when extended.

Question:6(i) Verify Euler’s formula for these solids.

(i) Euler formula F+V = E + 2.

So, Number of faces (F) = 7, Number of vertices (V) = 10 and number of edges (E) = 15.

Hence putting in the formula; we get,

7 + 10 = 15 + 2

17 = 17 hence, it satisfies the Euler formula.

Question:6(ii) Verify Euler’s formula for these solids. Answer:

(ii) Euler formula F+V = E + 2.

So, Number of faces (F) = 9, Number of vertices (V) = 9 and number of edges (E) = 16.

Hence putting in the formula; we get,

9 + 9 = 16 + 2

18 = 18 hence, it satisfies the Euler formula.

Question:7 Using Euler’s formula find the unknown.

We know the Euler Formula:

F + V = E + 2 :

hence we can easily find the unknown let say 'F, V, and E'

So, For Ist case:

F + 6 = 12 + 2 or F = 8, hence the number of faces in Ist case is 8.

For IInd Case;

5 + V = 9 + 2 or V = 6, hence the number of vertices in IInd case is 6.

For IIIrd case;

20 + 12 = E + 2 or E = 30, hence the number of Edges in the IIIrd case is 30.

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

Checking using Euler's Formula:

F + V = E +2;

Given that F = 10, V = 15 and E = 20 so,

Putting in equation: 10 + 15 = 35 and 20 +2 = 22

Hence, given polyhedron having 10 faces, 20 edges and 15 vertices is not possible.

## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes - Topics

• Views of 3D-Shapes
• Mapping Space Around Us
• Faces, Edges, and Vertices

## NCERT Solutions for Class 8 Maths - Chapter Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

## Key Features Of NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

Comprehensive Coverage: Solutions for maths chapter 10 class 8 cover all topics and concepts related to visualizing solid shapes as per the Class 8 syllabus.

Step-by-Step Solutions: Detailed, step-by-step explanations for each problem, making it easy for students to understand and apply mathematical concepts related to three-dimensional shapes.

Illustrations and Diagrams: These class 8 maths ch 10 question answer includes diagrams, figures, and illustrations to visually explain the properties, views, and representations of solid shapes.

## NCERT Solutions for Class 8 - Subject Wise

In NCERT solutions for class 8 maths chapter 10 visualizing solid shapes only one formula has been used know as Euler’s formula.

For any polyhedron-

$F+V-E=2$

where F - Number of faces

V - Number of vertices

E - Number of edges

As the name suggests this chapter is more about visualizing the shapes and drawing the front view, side view, and top view. In exercise 1 and 2 of NCERT solutions for class 8 maths chapter 10 visualizing solid shapes, most questions are related to visualizing shape and mapping which are explained with the help of drawing and graphs.

## NCERT Books and NCERT Syllabus

1. What are the important topics of NCERT book chapter Visualizing Solid Shapes ?

Views of the 3D-shapes, faces, edges and vertices are the important topics of this chapter.

2. How many chapters are there in the NCERT syllabus CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

3. Does CBSE provide NCERT solution for class 8 ?

No, CBSE doesn't provide NCERT solutions for any class and subject.

4. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

5. Where can I find the complete solutions of NCERT for class 8 maths ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

6. How does the NCERT solutions are helpful ?

NCERT solutions are provided in a very detailed manner so it will give the conceptual clarity to students as well it helps them in their homework.

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The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Visual Communication Designer

Individuals who want to opt for a career as a Visual Communication Designer will work in the graphic design and arts industry. Every sector in the modern age is using visuals to connect with people, clients, or customers. This career involves art and technology and candidates who want to pursue their career as visual communication designer has a great scope of career opportunity.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available

Advertising managers consult with the financial department to plan a marketing strategy schedule and cost estimates. We often see advertisements that attract us a lot, not every advertisement is just to promote a business but some of them provide a social message as well. There was an advertisement for a washing machine brand that implies a story that even a man can do household activities. And of course, how could we even forget those jingles which we often sing while working?

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

3 Jobs Available

A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

2 Jobs Available
##### Quality Systems Manager

A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party.

2 Jobs Available
##### Merchandiser

A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying.

2 Jobs Available
##### Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.

2 Jobs Available
##### Production Planner

Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner.

2 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### .NET Developer

.NET Developer Job Description: A .NET Developer is a professional responsible for producing code using .NET languages. He or she is a software developer who uses the .NET technologies platform to create various applications. Dot NET Developer job comes with the responsibility of  creating, designing and developing applications using .NET languages such as VB and C#.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### DevOps Architect

A DevOps Architect is responsible for defining a systematic solution that fits the best across technical, operational and and management standards. He or she generates an organised solution by examining a large system environment and selects appropriate application frameworks in order to deal with the system’s difficulties.

2 Jobs Available
##### Cloud Solution Architect

Individuals who are interested in working as a Cloud Administration should have the necessary technical skills to handle various tasks related to computing. These include the design and implementation of cloud computing services, as well as the maintenance of their own. Aside from being able to program multiple programming languages, such as Ruby, Python, and Java, individuals also need a degree in computer science.

2 Jobs Available