NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes.

Board	CBSE
Textbook	NCERT
Class	Class 8
Subject	Maths
Chapter	Chapter 10
Chapter Name	Visualising Solid Shapes
Exercise	Ex 10.1, Ex 10.2, Ex 10.3
Number of Questions Solved	16
Category	NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

Chapter 10 Visualising Solid Shapes Exercise 10.1

Question 1.
For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The first one is done for you.

Solution:
Matching for each solid to its corresponding top and front views is shown as under :

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


Solution:
For each solid the corresponding top, front and side views are identified as indicated by the respective figures :

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



Solution:
For each given solid, the top view, front view and side view are identified as indicated under the respective figures :

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


Solution:
The different views of the given objects are drawn as under :

Chapter 10 Visualising Solid Shapes Exercise 10.2

Question 1.
Look at the following map of a city

Answer the following :
(a) Colour the map as follows : Blue-Water, 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?
Solution:
The map is coloured as desired to complete part
(a) Green X and Y are marked at the desired place to complete part
(b) Short street route in red from Library to the bus depot is drawn to complete part
(c)

(d) City Park.
(e) Sr. Secondary School.

Question 2.
Draw a map of your class room using proper scale and symbols for different objects.
Solution:
Map of class room is as under :

Question 3.
Draw a map of your school compound using proper scale and symbols for various features like play ground, main building, garden, etc.
Solution:
Map of school compound showing various features like play ground, main building, garden, etc. is as under :

Question 4.
Draw a map giving instructions to your friend so that she reaches your house without any difficulty.
Solution:
A map giving instructions to my friend so that she reaches my house without any difficulty is as under :

Instructions :

1. Start from city park on Gandhi road.
2. Go forward on the Gandhi road.
3. From the library, go opposite to it.
4. After moving a few steps again you will find a Spencer’s store on your right hand side.
5. Start moving again from the store.
6. After a few steps, turn right.
7. On the way, you will find a primary school, now go opposite to it.
8. Move ahead and turn right after sweet shop.
9. You will find a fire station.
10. When you go straight, you will find my house.

Chapter 10 Visualising Solid Shapes Exercise 10.3

Question 1.
Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Solution:
Since a polyhedron is a solid, which is bounded by four or more polygonal faces in such a way that pairs of faces meet along edges and three or more edges meet in each vertex, therefore,
(i) A polyhedron cannot for its faces have three triangles.
(ii) A polyhedron can for its faces have four triangles.
(iii) A polyhedron can for its faces have a square and four triangles.

Question 2.
Is it possible to have a polyhedron with any given number of faces? (Hint : Think of a pyramid)
Solution:
Yes, it is possible only if the number of faces are greater than or equal to four.

Question 3.
Which are prisms among the following ?

Solution:
We know that a prism is a polyhedron, two of whose faces are congruent polygons in parallel planes and whose other faces are parallelograms. Therefore,
(i) A nail is not a prism.
(ii) An unsharpened pencil is a prism.
(iii) A table weight is not a prism.
(iv) A box is a prism.

Question 4.
(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Solution:
(i) A prism becomes a cylinder provided the number of sides of its base becomes larger and larger.
(ii) A pyramid becomes a cone provided the number of sides of its base becomes larger and larger.

Question 5.
Is a square prism same as a cube? Explain.
Solution:
Yes, it can be a cube. But it can be a cuboid also.

Question 6.
Verify Euler’s formula for these solids.

Solution:
(i) In this figure,
F = 7, V = 10, E =15
∴ F + V =7 + 10 = 17 and E + 2 =15 + 2 = 17
⇒ F+V=E+ 2
Hence, Euler’s formula is verified.

(ii) In this figure,
F =9, V = 9,E =16
∴ F + V =9 + 9 =18 and E + 2 =16 +2 =18
⇒ F + V =E + 2
Hence, Euler’s formula is verified.

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

Solution:
In 1st part : Faces = ?, Vertices =6, Edges =12
By Euler’s formula, we know that F + V= E + 2
⇒ F = E + 2 – V
= 12 + 2-6 =8
Hence, faces =8

In 2nd part : Faces = 5, Vertices = ?, Edges = 9
By Euler’s formula, we know that
F + V = E + 2
⇒ V = E + 2 – F = 9+ 2- 5 = 6
Hence, vertices =6

In 3rd part : Faces =20, Vertices =12, Edges =?
By Euler’s formula, we know that
F+V=E+2
⇒ E = F + V – 2 = 20 + 12 – 2 = 30
Hence, edges =30

Question 8.
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Solution:
Since F + V ≠ E +2 (as 10 +15 ≠ 20 + 2)
A polyhedron cannot have 10 faces, 20 edges and 15 vertices.

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