NCERT Solutions for Class 8 Maths Visualising Solid Shapes [Old Book]
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Page 1
NCERT
SOLUTIONS
CLASS - 8TH
aglase .co
SOLUTIONS
CLASS - 8TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Class : 8th
Subject : Maths
Chapter : 10
Chapter Name : Visualising Solid Shapes
Exercise 10.1
Q1 For each of the given solid, the two views are given. Match for each solid the
corresponding top and front views. The �rst one is done for you
Answer. The given solids, matched to their respective side view and top view, are as
follows.
Object Side view Top view
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Class : 8th
Subject : Maths
Chapter : 10
Chapter Name : Visualising Solid Shapes
Exercise 10.1
Q1 For each of the given solid, the two views are given. Match for each solid the
corresponding top and front views. The �rst one is done for you
Answer. The given solids, matched to their respective side view and top view, are as
follows.
Object Side view Top view
Page 1 of 13 Aglasem Schools
Page 3
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Page : 157 , Block Name : Exercise 10.1
Q2 For each of the given solid, the three views are given. Identify for each solid the
corresponding top, front and side views.
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Page : 157 , Block Name : Exercise 10.1
Q2 For each of the given solid, the three views are given. Identify for each solid the
corresponding top, front and side views.
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Page 4
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Answer.
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Answer.
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Page 5
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Page : 158 , Block Name : Exercise 10.1
Q3 For each given solid, identify the top view, front view and side view
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Page : 158 , Block Name : Exercise 10.1
Q3 For each given solid, identify the top view, front view and side view
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Page 6
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Answer.
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Answer.
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Page 7
Book : Mathematics Ncert Solutions | Chapter-10 Maths
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Page 6 of 13 Aglasem Schools
Page 8
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Page : 159 , Block Name : Exercise 10.1
Q4 Draw the front view, side view and top view of the given objects.
Answer.
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Page : 159 , Block Name : Exercise 10.1
Q4 Draw the front view, side view and top view of the given objects.
Answer.
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Page 9
Book : Mathematics Ncert Solutions | Chapter-10 Maths
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Page 8 of 13 Aglasem Schools
Page 10
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Page : 160 , Block Name : Exercise 10.1
Exercise 10.2
Q1 Look at the given map of a city.
Answer the following.
(a) Colour the map as follows: Blue-water, red-�re 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 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?
Answer. (a) The given map coloured in the required way is as follows.
(b)The marks can be put at the given points as follows.
(c) The shortest route from the library to bus depot is represented by red colour.
Page 9 of 13 Aglasem Schools
Page : 160 , Block Name : Exercise 10.1
Exercise 10.2
Q1 Look at the given map of a city.
Answer the following.
(a) Colour the map as follows: Blue-water, red-�re 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 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?
Answer. (a) The given map coloured in the required way is as follows.
(b)The marks can be put at the given points as follows.
(c) The shortest route from the library to bus depot is represented by red colour.
Page 9 of 13 Aglasem Schools
Page 11
Book : Mathematics Ncert Solutions | Chapter-10 Maths
(d) Between the Market and the City Park, the City Park is further east.
(e) Between the Primary School and the Sr. Secondary School, the Sr. Secondary
School is further south.
Page : 163 , Block Name : Exercise 10.2
Q2 Draw a map of your classroom using proper scale and symbols for different objects.
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Q3 Draw a map of your school compound using proper scale and symbols for various
features like play ground main building, garden etc
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Q4 Draw a map giving instructions to your friend so that she reaches your house without
any dif�culty
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Exercise 10.3
Q1 Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Answer. (i) No, such a polyhedron is not possible. A polyhedron has minimum 4 faces.
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(d) Between the Market and the City Park, the City Park is further east.
(e) Between the Primary School and the Sr. Secondary School, the Sr. Secondary
School is further south.
Page : 163 , Block Name : Exercise 10.2
Q2 Draw a map of your classroom using proper scale and symbols for different objects.
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Q3 Draw a map of your school compound using proper scale and symbols for various
features like play ground main building, garden etc
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Q4 Draw a map giving instructions to your friend so that she reaches your house without
any dif�culty
Answer. DIY
Page : 163 , Block Name : Exercise 10.2
Exercise 10.3
Q1 Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Answer. (i) No, such a polyhedron is not possible. A polyhedron has minimum 4 faces.
Page 10 of 13 Aglasem Schools
Page 12
Book : Mathematics Ncert Solutions | Chapter-10 Maths
(ii) Yes, a triangular pyramid has 4 triangular faces.
(iii) Yes, a square pyramid has a square face and 4 triangular faces.
Page : 166 , Block Name : Exercise 10.3
Q2 Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a
pyramid).
Answer. A polyhedron has a minimum Of 4 faces.
Page : 166 , Block Name : Exercise 10.3
Q3 Which are prisms among the following?
Answer. (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) It is not a prism. It is a pyramid.
(iv) It is a prism.
Page : 166 , Block Name : Exercise 10.3
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(ii) Yes, a triangular pyramid has 4 triangular faces.
(iii) Yes, a square pyramid has a square face and 4 triangular faces.
Page : 166 , Block Name : Exercise 10.3
Q2 Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a
pyramid).
Answer. A polyhedron has a minimum Of 4 faces.
Page : 166 , Block Name : Exercise 10.3
Q3 Which are prisms among the following?
Answer. (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) It is not a prism. It is a pyramid.
(iv) It is a prism.
Page : 166 , Block Name : Exercise 10.3
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Page 13
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Q4 (i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Answer. (i) A cylinder can be thought of as a circular prism i.e., a prism that has a circle
as its base.
(ii) A cone can be thought of as a circular pyramid i.e., a pyramid that has a circle as
its base.
Page : 166 , Block Name : Exercise 10.3
Q5 Is a square prism same as a cube? Explain.
Answer. A square prism has a square as its base. However, its height is not necessarily
same as the side of the square. Thus, a square prism can also be a cuboid.
Page : 166 , Block Name : Exercise 10.3
Q6 Verify Euler’s formula for these solids.
Answer. (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, Euler's formula is veri�ed.
(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, Euler's formula is veri�ed.
Page : 166 , Block Name : Exercise 10.3
Q7 Using Euler’s formula �nd the unknown
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Q4 (i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Answer. (i) A cylinder can be thought of as a circular prism i.e., a prism that has a circle
as its base.
(ii) A cone can be thought of as a circular pyramid i.e., a pyramid that has a circle as
its base.
Page : 166 , Block Name : Exercise 10.3
Q5 Is a square prism same as a cube? Explain.
Answer. A square prism has a square as its base. However, its height is not necessarily
same as the side of the square. Thus, a square prism can also be a cuboid.
Page : 166 , Block Name : Exercise 10.3
Q6 Verify Euler’s formula for these solids.
Answer. (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, Euler's formula is veri�ed.
(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, Euler's formula is veri�ed.
Page : 166 , Block Name : Exercise 10.3
Q7 Using Euler’s formula �nd the unknown
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Page 14
Book : Mathematics Ncert Solutions | Chapter-10 Maths
Answer. 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
Page : 167 , Block Name : Exercise 10.3
Q8 Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Answer. Number of faces = F = 10
Number of edges = E = 20
Number of vertices = V = 15
Any polyhedron satis�es Euler's Formula, according to which, F + V - E = 2
For the given polygon,
F + V − E = 10 + 15 − 20 = 25 − 20 = 5 ≠ 2
Since Euler’s formula is not satis�ed, such a polyhedron is not possible.
Page : 167 , Block Name : Exercise 10.3
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Answer. 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
Page : 167 , Block Name : Exercise 10.3
Q8 Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Answer. Number of faces = F = 10
Number of edges = E = 20
Number of vertices = V = 15
Any polyhedron satis�es Euler's Formula, according to which, F + V - E = 2
For the given polygon,
F + V − E = 10 + 15 − 20 = 25 − 20 = 5 ≠ 2
Since Euler’s formula is not satis�ed, such a polyhedron is not possible.
Page : 167 , Block Name : Exercise 10.3
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Document Details
| Board / Org | NCERT |
| Exam | Class 8 |
| Type | Solution |
| Pages | 14 |
| Language | english |
| Updated | 22 Jul 2026 |