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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
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FAQs on NCERT Textbook- Visualising Solid Shapes - NCERT Textbooks (Class 6 to Class 12) - CTET & State TET

1. What is the importance of visualizing solid shapes in mathematics?
Ans. Visualizing solid shapes in mathematics is important because it helps us understand and analyze three-dimensional objects. It allows us to visualize the shape, size, and orientation of objects in space, making it easier to solve problems related to geometry and spatial reasoning.
2. How can visualizing solid shapes be applied in real-life situations?
Ans. Visualizing solid shapes can be applied in various real-life situations. For example, architects and engineers use it to design buildings and structures. Artists use it to create sculptures and 3D models. It is also useful in fields like computer graphics, manufacturing, and even in everyday activities like packing objects efficiently in a box.
3. What are the different methods to visualize solid shapes?
Ans. There are several methods to visualize solid shapes. One common method is to use models or physical objects that represent the shape, such as cubes, pyramids, or spheres. Another method is to draw two-dimensional representations of the shape on paper, with different views showing different sides of the object. Additionally, computer software and simulations can be used to create virtual 3D models that can be rotated and viewed from different angles.
4. How does visualizing solid shapes help in understanding spatial relationships?
Ans. Visualizing solid shapes helps in understanding spatial relationships by allowing us to perceive the position, direction, and orientation of objects in relation to one another. By mentally manipulating and rotating the shapes in our mind, we can determine how they fit together, identify their faces, edges, and vertices, and understand how they interact with each other in space.
5. Are there any specific techniques or strategies to improve the ability to visualize solid shapes?
Ans. Yes, there are techniques and strategies to improve the ability to visualize solid shapes. One way is to practice mentally rotating and manipulating different shapes in your mind. Another way is to use physical objects or models to explore and understand different shapes. Additionally, engaging in activities that involve spatial reasoning, such as puzzles, construction games, and 3D modeling, can also help enhance visualization skills.
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