- 3D objects have different views from different positions.
- Front, side and top view are the different views that one will study in this chapter through cubical blocks and 3-dimensional shapes.
- A map depicts the location of a particular object/place in relation to other objects/places.
- Symbols are used to depict the different objects/places.
- Faces
- Edges
- Vertex
- Polyhedron
- Non-polyhedron
- Convex polyhedron
- Regular polyhedrons
- Prism
- Pyramids
F + V = E + 2
where F stands for number of faces, V stands for number of vertices and E stands for number of edges.
Three unsolved exercises are given for the assessment of students. The last exercise is 10.3 consisting of 8 questions. Questions are given in different patterns which makes the exercise more attractive and interesting for students.
9 points are listed in the summary of chapter in the end.
Page No 157:
Question 1:
For each of the given solid, the two views are given. Match for each solid the corresponding top and front views.
Answer:
The given solids, matched to their respective side view and top view, are as follows.
Object Side view Top view
Page No 158:
Question 2:
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.
Answer:
(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
Page No 159:
Question 3:
For each given solid, identify the top view, front view and side view.
(a)
(b)
(c)
(d)
(e)
Answer:
(a)
(i) Top (ii) Front/Side (iii) Side/Front
(b)
(i) Side (ii) Front (iii) Top
(c)
(i) Top (ii) Side (iii) Front
(d)
(i) Side (ii) Front (iii) Top
(e)
(i) Front/Side (ii) Top (iii) Side/Front
Page No 160:
Question 4:
Draw the front view, side view and top view of the given objects.
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(a) A military tent |
(b) A table |
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(c) A nut |
(d) A hexagonal block |
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(e) A dice |
(f) A solid |
Answer:
(a)
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A military tent |
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Front View |
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Top View |
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Side View |
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(b)
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A table |
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Front View |
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Top View |
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Side View |
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(c)
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A nut |
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Front View |
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Top View |
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Side View |
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(d)
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A hexagonal block |
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Front View |
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Top View |
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Side View |
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(e)
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A dice |
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Front View |
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Top View |
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Side View |
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(f)
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A solid |
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Front View |
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Top View |
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Side View |
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Page No 163:
Question 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 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.
(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.
Video Solution for visualising solid shapes (Page: 163 , Q.No.: 1)
NCERT Solution for Class 8 math - visualising solid shapes 163 , Question 1
Page No 166:
Question 1:
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.
(ii) Yes, a triangular pyramid has 4 triangular faces.
(iii) Yes, a square pyramid has a square face and 4 triangular faces.
Page No 166:
Question 2:
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 No 166:
Question 3:
Which are prisms among the following?
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(i) |
(ii) |
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(iii) |
(iv) |
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 No 166:
Question 4:
(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 No 166:
Question 5:
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.
Video Solution for visualising solid shapes (Page: 166 , Q.No.: 5)
NCERT Solution for Class 8 math - visualising solid shapes 166 , Question 5
Page No 166:
Question 6:
Verify Euler’s formula for these solids.
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(i) |
(ii) |
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 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, Euler’s formula is verified.
Video Solution for visualising solid shapes (Page: 166 , Q.No.: 6)
NCERT Solution for Class 8 math - visualising solid shapes 166 , Question 6
Page No 167:
Question 7:
Using Euler’s formula, find the unknown.
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Faces |
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5 |
20 |
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Vertices |
6 |
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12 |
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Edges |
12 |
9 |
? |
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
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Faces |
8 |
5 |
20 |
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Vertices |
6 |
6 |
12 |
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Edges |
12 |
9 |
30 |
Video Solution for visualising solid shapes (Page: 167 , Q.No.: 7)
NCERT Solution for Class 8 math - visualising solid shapes 167 , Question 7
Page No 167:
Question 8:
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 satisfies 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 satisfied, such a polyhedron is not possible.
View NCERT Solutions for all chapters of Class 8