NCERT Solutions for Class 8 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.

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

Object Side view Top view

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

Ans:

(a)

(i) Front

(ii) Side 

(iii) Top

(b)

(i) Side 

(ii) Front

(iii) Top

(c)

(i) Front

(ii) Side

(iii) Top

(d)

(i) Front

(ii) Side

(iii) Top

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

(a) 

Ans: (a)

(i) Top

(ii) Front/Side 

(iii) Side/Front 

(b)

Ans: (b)

(i) Side

(ii) Front

(iii) Top

(c)

Ans:

(i) Top

(ii) Side

(iii) Front 

(d)

 Ans:

(i) Side

(ii) Front 

(iii) Top

(e)

Ans:

(i) Front/Side 

(ii) Top 

(iii) Side/Front

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

(a) A military tent

Front view
Top view
Side view

(b) A table

Front view
Top view
Side view

(c) A nut

Front view
Top view
Side view

(d) A hexagonal block

Front view
Top view
Side view

(d) A dice

Front view
Top view
Side view

(f) A solid

Front view
Top view
Side view

Exercise 10.2 

1. Look at the given map of a city. 

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. 

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

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

(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.

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

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)

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

(b)

Ans (b)  Yes, It is a prism

(c)

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

(d)

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)

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)

(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. 

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: 

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 –

Exercise 10.1

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.

Exercise 10.2

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.

Exercise 10.3

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 Vedantu’s subject experts.

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• Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

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Conclusion

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