NCERT Textbook- Visualising Solid Shapes | NCERT Textbooks (Class 6 to Class 12) - CTET & State TET PDF Download

 Page 1


VISUALISING SOLID SHAPES  153
DO THIS
10.1  Introduction
In Class VII, you have learnt about plane shapes and solid shapes. Plane shapes have two
measurements like length and breadth and therefore they are called two-dimensional shapes
whereas a solid object has three measurements like length, breadth, height or depth. Hence,
they are called three-dimensional shapes. Also, a solid object occupies some space.
T wo-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-
D figures. Y ou may recall that triangle, rectangle, circle etc., are 2-D figures while cubes,
cylinders, cones, spheres etc. are three-dimensional figures.
Match the following: (First one is done for you)
Shape Type of Shape Name of the shape
3-dimensional Sphere
2-Dimensional Cylinder
3-dimensional Square
2-dimensional Circle
Visualising Solid
Shapes
CHAPTER
10
2022-23
Page 2


VISUALISING SOLID SHAPES  153
DO THIS
10.1  Introduction
In Class VII, you have learnt about plane shapes and solid shapes. Plane shapes have two
measurements like length and breadth and therefore they are called two-dimensional shapes
whereas a solid object has three measurements like length, breadth, height or depth. Hence,
they are called three-dimensional shapes. Also, a solid object occupies some space.
T wo-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-
D figures. Y ou may recall that triangle, rectangle, circle etc., are 2-D figures while cubes,
cylinders, cones, spheres etc. are three-dimensional figures.
Match the following: (First one is done for you)
Shape Type of Shape Name of the shape
3-dimensional Sphere
2-Dimensional Cylinder
3-dimensional Square
2-dimensional Circle
Visualising Solid
Shapes
CHAPTER
10
2022-23
154  MATHEMATICS
DO THIS
Match the following pictures (objects) with their shapes:
3-dimensional Cuboid
3- dimensional Cube
2-dimensional Cone
3-dimensional T riangle
Note that all the above shapes are single. However, in our practical life, many a times, we
come across combinations of different shapes. For example, look at the following objects.
A tent A tin Softy (ice-cream)
A cone surmounted A cylinderical shell A cone surmounted by a
on a cylinder hemisphere
A photoframe A bowl Tomb on a pillar
A rectangular path A hemispherical shell Cylinder surmounted
by a hemisphere
Picture (object) Shape
(i) An agricultural  field T wo rectangular cross paths inside a
rectangular park.
2022-23
Page 3


VISUALISING SOLID SHAPES  153
DO THIS
10.1  Introduction
In Class VII, you have learnt about plane shapes and solid shapes. Plane shapes have two
measurements like length and breadth and therefore they are called two-dimensional shapes
whereas a solid object has three measurements like length, breadth, height or depth. Hence,
they are called three-dimensional shapes. Also, a solid object occupies some space.
T wo-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-
D figures. Y ou may recall that triangle, rectangle, circle etc., are 2-D figures while cubes,
cylinders, cones, spheres etc. are three-dimensional figures.
Match the following: (First one is done for you)
Shape Type of Shape Name of the shape
3-dimensional Sphere
2-Dimensional Cylinder
3-dimensional Square
2-dimensional Circle
Visualising Solid
Shapes
CHAPTER
10
2022-23
154  MATHEMATICS
DO THIS
Match the following pictures (objects) with their shapes:
3-dimensional Cuboid
3- dimensional Cube
2-dimensional Cone
3-dimensional T riangle
Note that all the above shapes are single. However, in our practical life, many a times, we
come across combinations of different shapes. For example, look at the following objects.
A tent A tin Softy (ice-cream)
A cone surmounted A cylinderical shell A cone surmounted by a
on a cylinder hemisphere
A photoframe A bowl Tomb on a pillar
A rectangular path A hemispherical shell Cylinder surmounted
by a hemisphere
Picture (object) Shape
(i) An agricultural  field T wo rectangular cross paths inside a
rectangular park.
2022-23
VISUALISING SOLID SHAPES  155
(ii) A groove A circular path around a circular ground.
(iii) A toy A triangular field adjoining a square field.
(iv) A circular park A cone taken out of a cylinder.
(v) A cross path A hemisphere surmounted on a cone.
10.2  Views of 3D-Shapes
Y ou have learnt that a 3-dimensional object can look differently from different positions so
they can be drawn from different perspectives. For example, a given hut can have the
following views.
A hut Front view Side view Top view
similarly , a glass can have the following views.
A glass Side view Top view
Why is the top view of the glass a pair of concentric circles? Will the side view appear different if taken from
some other direction? Think about this! Now look at the different views of a brick.
T op
Side Front
2022-23
Page 4


VISUALISING SOLID SHAPES  153
DO THIS
10.1  Introduction
In Class VII, you have learnt about plane shapes and solid shapes. Plane shapes have two
measurements like length and breadth and therefore they are called two-dimensional shapes
whereas a solid object has three measurements like length, breadth, height or depth. Hence,
they are called three-dimensional shapes. Also, a solid object occupies some space.
T wo-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-
D figures. Y ou may recall that triangle, rectangle, circle etc., are 2-D figures while cubes,
cylinders, cones, spheres etc. are three-dimensional figures.
Match the following: (First one is done for you)
Shape Type of Shape Name of the shape
3-dimensional Sphere
2-Dimensional Cylinder
3-dimensional Square
2-dimensional Circle
Visualising Solid
Shapes
CHAPTER
10
2022-23
154  MATHEMATICS
DO THIS
Match the following pictures (objects) with their shapes:
3-dimensional Cuboid
3- dimensional Cube
2-dimensional Cone
3-dimensional T riangle
Note that all the above shapes are single. However, in our practical life, many a times, we
come across combinations of different shapes. For example, look at the following objects.
A tent A tin Softy (ice-cream)
A cone surmounted A cylinderical shell A cone surmounted by a
on a cylinder hemisphere
A photoframe A bowl Tomb on a pillar
A rectangular path A hemispherical shell Cylinder surmounted
by a hemisphere
Picture (object) Shape
(i) An agricultural  field T wo rectangular cross paths inside a
rectangular park.
2022-23
VISUALISING SOLID SHAPES  155
(ii) A groove A circular path around a circular ground.
(iii) A toy A triangular field adjoining a square field.
(iv) A circular park A cone taken out of a cylinder.
(v) A cross path A hemisphere surmounted on a cone.
10.2  Views of 3D-Shapes
Y ou have learnt that a 3-dimensional object can look differently from different positions so
they can be drawn from different perspectives. For example, a given hut can have the
following views.
A hut Front view Side view Top view
similarly , a glass can have the following views.
A glass Side view Top view
Why is the top view of the glass a pair of concentric circles? Will the side view appear different if taken from
some other direction? Think about this! Now look at the different views of a brick.
T op
Side Front
2022-23
156  MATHEMATICS
DO THIS
A brick Front view Side view Top view
We can also get different views of figures made by joining cubes. For example.
Solid Side view Front view Top view
made of three cubes
Solid Top view Front view Side view
made of four cubes
Solid Side view Front view Top view
made of four cubes
Observe different things around you from different positions. Discuss with your friends
their various views.
T op
Side
Front
Side
Front
T op
Front
Side
T op
T op
Side
Front
2022-23
Page 5


VISUALISING SOLID SHAPES  153
DO THIS
10.1  Introduction
In Class VII, you have learnt about plane shapes and solid shapes. Plane shapes have two
measurements like length and breadth and therefore they are called two-dimensional shapes
whereas a solid object has three measurements like length, breadth, height or depth. Hence,
they are called three-dimensional shapes. Also, a solid object occupies some space.
T wo-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-
D figures. Y ou may recall that triangle, rectangle, circle etc., are 2-D figures while cubes,
cylinders, cones, spheres etc. are three-dimensional figures.
Match the following: (First one is done for you)
Shape Type of Shape Name of the shape
3-dimensional Sphere
2-Dimensional Cylinder
3-dimensional Square
2-dimensional Circle
Visualising Solid
Shapes
CHAPTER
10
2022-23
154  MATHEMATICS
DO THIS
Match the following pictures (objects) with their shapes:
3-dimensional Cuboid
3- dimensional Cube
2-dimensional Cone
3-dimensional T riangle
Note that all the above shapes are single. However, in our practical life, many a times, we
come across combinations of different shapes. For example, look at the following objects.
A tent A tin Softy (ice-cream)
A cone surmounted A cylinderical shell A cone surmounted by a
on a cylinder hemisphere
A photoframe A bowl Tomb on a pillar
A rectangular path A hemispherical shell Cylinder surmounted
by a hemisphere
Picture (object) Shape
(i) An agricultural  field T wo rectangular cross paths inside a
rectangular park.
2022-23
VISUALISING SOLID SHAPES  155
(ii) A groove A circular path around a circular ground.
(iii) A toy A triangular field adjoining a square field.
(iv) A circular park A cone taken out of a cylinder.
(v) A cross path A hemisphere surmounted on a cone.
10.2  Views of 3D-Shapes
Y ou have learnt that a 3-dimensional object can look differently from different positions so
they can be drawn from different perspectives. For example, a given hut can have the
following views.
A hut Front view Side view Top view
similarly , a glass can have the following views.
A glass Side view Top view
Why is the top view of the glass a pair of concentric circles? Will the side view appear different if taken from
some other direction? Think about this! Now look at the different views of a brick.
T op
Side Front
2022-23
156  MATHEMATICS
DO THIS
A brick Front view Side view Top view
We can also get different views of figures made by joining cubes. For example.
Solid Side view Front view Top view
made of three cubes
Solid Top view Front view Side view
made of four cubes
Solid Side view Front view Top view
made of four cubes
Observe different things around you from different positions. Discuss with your friends
their various views.
T op
Side
Front
Side
Front
T op
Front
Side
T op
T op
Side
Front
2022-23
VISUALISING SOLID SHAPES  157
EXERCISE 10.1
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.
Object Side view Top view
(a) (i) (i)
     A bottle
(b) (ii) (ii)
    A weight
(c) (iii) (iii)
A flask
(d) (iv) (iv)
Cup and Saucer
(e) (v) (v)
Container
2022-23