NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes


Chapter 10 of Visualising Solid Shapes includes both solid and planar shapes with its various features. Students have to study Polyhedron, Prism, Pyramid, Tetrahedron apart from 3-D shapes. If grasped properly, students would find it easy to score high marks on questions from these topics in examination. NCERT solutions for class 8 Maths chapter 10 would be useful for students in that regard. 

While the chapter on Visualising Solid Shapes can be quite easy for students, they would need to do a consistent revision to be familiar with all the aspects of the topic. Moreover, the topic of Mapping is new to students. Hence, greater clarity would be needed on that. Students can download the PDF of chapter 10 Maths class 8 NCERT Solution from CoolGyan’s official website, and study those offline at their convenience. Download NCERT Solutions for Class 8 Science to score more marks in your examinations.

Access NCERT solutions for Maths Chapter 10 – Visualising Solid Shapes

Exercise 10.1

1. For each of the given solids, the two views are given. Match for each solid the corresponding top and front views.

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Ans: The following is the solid that have been matched to their corresponding side and top views.

Object Side view Top view

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 2. For each of the given solids, the three views are given. Identify for each solid the corresponding top, front and side views.

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Ans:

(a)

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(i) Front

(ii) Side 

(iii) Top

(b)

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(i) Side 

(ii) Front

(iii) Top

(c)

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(i) Front

(ii) Side

(iii) Top

(d)

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(i) Front

(ii) Side

(iii) Top

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

(a) 

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Ans: (a)

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(i) Top

(ii) Front/Side 

(iii) Side/Front 

(b)

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Ans: (b)

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(i) Side

(ii) Front

(iii) Top

(c)

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Ans:

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(i) Top

(ii) Side

(iii) Front 

(d)

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 Ans:

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(i) Side

(ii) Front 

(iii) Top

(e)

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Ans:

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(i) Front/Side 

(ii) Top 

(iii) Side/Front

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

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(a) A military tent

Front view

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Top view

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Side view

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(b) A table

Front view

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Top view

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Side view

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(c) A nut

Front view

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Top view

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Side view

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(d) A hexagonal block

Front view

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Top view

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Side view

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(d) A dice

Front view

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Top view

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Side view

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(f) A solid

Front view

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Top view

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Side view

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Exercise 10.2 

1. Look at the given map of a city. 

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Answer The Following. 

(a) Colour the map as follows: Blue − water plant, red − fire station, orange − library, yellow − schools, green − park, pink − college, purple − hospital, brown − cemetery. 

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

(c) In red, draw a short street route from the library to the bus depot. 

(d) Which is further east, the city park or the market? 

(e) Which is further south, the Primary School or the Sr. Secondary School?

Ans: (a) The following is the given map, coloured in the desired manner. 

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(b) Marks can be placed at the following locations.

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(c) The red colour represents the shortest route from the library to the bus depot.

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(d) Between the Market and the City Park, the City Park is further east

(e) The Sr. Secondary School located further south between the Primary School and the Sr. Secondary School.

Exercise 10.3 

1. 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 doesn't exist. A polyhedron has at least four faces. 

(ii) A triangular pyramid does have four triangular faces.

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(iii) Yes, A square pyramid does, in fact, have a square face as well as four triangular faces.

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

Ans: A polyhedron has at least four faces.

3. Which are prisms among the following? 

(a)

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Ans (a) Because it has a curved surface, it is not a polyhedron. As a result, it will not be a prism.

(b)

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Ans (b)  Yes, It is a prism

(c)

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 And (c) It is a pyramid,it is not a prism. 

(d)

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Ans (d)  Yes, It is a prism

4. (i) How are prisms and cylinders alike? 

Ans: (i)A cylinder can be compared to a circular prism that is a prism which has a circle as its base. 

(ii) How are pyramids and cones alike? 

(ii) A cone can be compared to a circular pyramid, that is, a pyramid with a circle as its base.

5. Is a square prism the same as a cube? Explain

Ans: The base of a square prism is a square. Its height, on the other hand, is not always the same as one of the square's sides. As a result, a square prism can also be a cuboid. 

6. Verify Euler’s formula for these solids. 

(i)

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Ans (i) Here, 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, Euler’s formula is verified. 

(ii)

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(ii) Here, Number of faces = F = $9$ 

Number of vertices = V = $9$

Number of edges = E = $16$ 

We have, F + V − E 

= $9+9-16$

 =$18-16$ 

= $2$

Hence, Euler’s formula is verified.

7. Using Euler’s formula, find the unknown. 

Faces

?

$5$

$20$

Vertices

$6$

?

$12$

Edges

$12$

$9$

?


Ans: Here,

By Euler’s formula, we have 

$F+V-E=3$

(i) $F+6-12=2$

$F-6=3$

$F=8$

(ii) $5+V-9=2$

$V-4=2$ 

$V=6$

(iii) $20+12-E=2$

$32-E=2$ 

$E=30$  

So, the completed table as follows: 

Faces

$8$

$5$

$20$

Vertices

$6$

$6$

$12$

Edges

$12$

$9$

$30$


8. 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 = $V=15$

Any polyhedron satisfies Euler’s Formula, according to which, $F+V-E=2$

For the given polygon, 

$F+V-E$

=$10+15-20$

= $25-20$

 =$5\ne 2$

Here, Euler’s formula is not satisfied, So a polyhedron is not possible.

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes - PDF Download

NCERT Solutions for Class 8 Maths Chapter 10

Few of the questions included in NCERT solutions class 8 Maths chapter 10 are –

Various shapes are given in the exercise, and the top and bottom view of the same should be matched. For each of the given solid, two corresponding views are given. In the next question, three views – top view, front view, and side views are given.

The shapes that are given in all these questions range from a hexagonal block, cube and dice. Another question puts across a picture of different objects, and the specific shape has to be identified. The main objects are a hexagonal block, a dice and a solid.

NCERT solutions for class 8 Maths chapter 10 illustrate a map in which students have to mark different components. For instance, different map components like water plant, fire station, library, schools, park, college, hospital, and cemetery have to be coloured in blue, red, orange, yellow, green, pink, purple, brown respectively. Students would also have to denote intersections of road.

Furthermore, students would also have to mark the location and direction of different points on the map. For example, further south to the Primary school have to be found out.

Objective questions are included in this section. There are multiple-choice questions with more than one correct answer. An example of a question – Can a polyhedron have for its faces – (a) Four triangles, (b) Three triangles, (c) Four triangles and a square. It can be understood from this question that option (b) and (c) are correct.

Students should ensure that they have a clear understanding of the topic of Visualising Solid Shapes, and to that end, NCERT solutions for class 8 Maths chapter 10 can be effective. However, should they face any problem in studying the chapter; they can always reach out to CoolGyan’s subject experts.

FAQs (Frequently Asked Questions)

1. What are the advantages of studying from NCERT class 8 Maths chapter 10?

NCERT solutions for class 8 Maths ch 10 by CoolGyan adopts simple and easy techniques in providing accurate answers, and those adhere to the latest CBSE guidelines and curriculum. 

Moreover, domain experts having considerable experience have been engaged to frame the solution. It has been ensured that there is an in-depth explanation given in a step-wise manner.

2. What are the topics included in NCERT solution class 8 Maths chapter 10?

The different topics discussed in NCERT solution for class 8 Maths chapter 10 are – (1) Introduction to the topic, (2) Views of 3-D Shapes, (3) Mapping Space Around Us, and (4) Faces, Edges, and Vertices. 

Moreover, there the questions come in various formats. The solutions to Exercise 10.1 include 4 short questions, Exercise 10.2 includes 3 short questions and 1 long question, Exercise 10.3 includes 8 short questions.

3. What is the best way to prepare NCERT Maths class 8 chapter 10 Visualising Solid Shapes?

One of the key aspects of preparing NCERT class 8 Maths chapter 10 solutions is to visualise the topic. Given that the chapter deals with solid shapes and plane shapes, it is important to conceptualise the differentiating factors at the outset. 

Start with the basics of various dimensions of figures and shapes. All the topics are interconnected, and their inter-relationships should be conceptualised. If students start to solve sums while studying the topic, it becomes easier for them to understand. Refer to the solved examples as well apart from consistently using graphical representation and diagrams as indicated in Maths NCERT solutions class 8 chapter 10.

4. What is the method for downloading the NCERT Solutions for Chapter 10 of Class 8 Maths?

The steps given below will help students in getting the NCERT Solutions for Chapter 10 of Class 8 Maths:

  • Visit the page NCERT Solutions for Chapter 10 of Class 8 Maths will be available.

  • Tap on the option of “Download PDF” which is above the PDF file.

  • The file will get downloaded and you can study offline.

5. What is Euler's Formula according to Chapter 10 of Class 8 Maths?

Euler's formula is used to find the unknown quantity of a polyhedron. It is described as the relationship between the faces, edges and vertices of a 3-D object.

The formula is given below:

F + V – E = 2

Here, F stands for the number of faces, vertices of the polyhedron are denoted by V and E is for the number of edges of the 3-D object.

Using this formula, we can find out any of the missing properties of the polyhedron.

6. What are polyhedrons and their types, according to Chapter 10 of Class 8 Maths?

The 3-D shapes with sharp corners, flat faces and straight edges are termed polyhedrons. The types of polyhedron are as follows:

  • Regular polyhedron –These are also known as platonic solids.

  • Irregular polyhedrons – In these polyhedrons, the faces are not congruent to each other.

  • Convex polyhedron –The convex polygon is known as a convex polyhedron. The line joining the two points lies inside the polyhedron.

  • Concave polyhedron – In this type of polyhedron, the line joining the two points on the surface lies outside the polyhedron.

7. How many types of regular polyhedrons are there in Chapter 10 of Class 8 Maths?

Regular polyhedrons are of five types. These are listed below:

  • Tetrahedron –This polyhedron has four vertices, six edges and four faces. Each face resembles an equilateral triangle.

  • Cube – There are eight vertices, six faces and 12 edges in a cube. The shape of the face is square.

  • Regular Octahedron –This 3-D shape has 12 edges, six vertices and eight faces. In this shape, each face is an equilateral triangle.

  • Regular Dodecahedron –Each face of this polyhedron is a regular pentagon. It has 30 edges, 20 vertices and 12 faces.

  • Regular Icosahedron –Equilateral triangle is the shape of each face of this polyhedron. It has 30 edges, 12 vertices and 20 faces.

8. Is Chapter 10 of Class 8 Maths easy?

“Visualising Solid Shapes” is Chapter 10 of Class 8 Maths. This Chapter is very easy as it talks about different shapes. Therefore, students will not find any difficulty while studying this chapter. But they should focus on this chapter to have a strong grip. They should prepare this chapter from the NCERT book. Solve the NCERT questions to understand the concepts. Attend all your school classes so that you don't miss out on any of the topics. Students can also take help of the NCERT Solutions available free of cost on the CoolGyan website and on the CoolGyan app.