15
Visualising Solid Shapes
inTroduCTion
In our daily life, we see several objects like books, balls, tubelights, ice cream cones etc., around
us which have different shapes. The common thing about most of these objects is that they have
length, breadth and height. These objects occupy space and have three-dimensions. Hence, these
are called three-dimensional (3-D) shapes.
In class VI, we have learnt about some of these three-dimensional shapes. In this chapter, we shall
try to know more about these three-dimensional shapes. We shall learn about nets for building
three-dimensional shapes, drawing solids on a flat surface (oblique sketches and isometric sketches)
and viewing different sections of a solid.
differenT solid shapes
Cuboid
The adjoining figure shows a cuboid. A brick, a book, a chalkbox, a matchbox and a tea packet are all examples of this shape.
faces, edges and Vertices
We have already learnt about faces, edges and vertices of solid shapes. Here we see them for a
cuboid:
Vertex
Face
Edge
A cuboid has six rectangular faces, twelve edges and eight vertices (corners).
Cube
A cuboid in which length, breadth and height are all equal is called a cube.
In a cube, all its six faces are squares.
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Prism
A (right) prism is a solid which has two identical top and bottom
faces (called bases) with their corresponding sides parallel. The other
faces are rectangular.
The shape of the prism is described by using the shape of the bases.
The adjoining diagram shows a ‘triangular prism’.
A triangular prism has 5 faces (2 triangular faces and 3 rectangular
faces), 9 edges and 6 vertices.
Base
Pyramid
A pyramid is a sold in which the vertices of one face (called base)
are joined by edges to one other vertex (called common vertex or
apex). The base is a polygon and all other faces are triangular.
The shape of the pyramid is described by using the shape of the base.
The adjoining diagram shows a triangular pyramid.
A triangular pyramid has 4 triangular faces, 6 edges and 4 vertices.
Base
The adjoining figure shows a rectangular pyramid.
Base
A rectangular pyramid has 5 faces (1 rectangular face and 4 triangular faces), 8 edges and
5 vertices.
Tetrahedron
It is a special triangular pyramid whose base and all faces are equilateral triangles of same size.
Sphere
The adjoining figure shows a sphere. It has only one face which
is curved. A football, a tennis ball, a cricket ball are all examples
of this shape.
Cylinder
The adjoining figure shows a (right circular) cylinder.
A tubelight, a road roller are examples of a right circular cylinder.
A right circular cylinder has 2 plane (circular) faces, one curved face
and two curved edges. Curved edges are circles of equal radii.
Curved
edge
Curved
face
Plane
face
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Note. Cuboid, cube and (right circular) cylinder are special types of
right prisms.
Vertex
Cone
A clown’s cap, an ice cream cone are examples of (right circular) cones.
A (right circular) cone has one plane (circular) face, one curved face, one
vertex and one curved edge. Curved edge is a circle.
Curved
face
Plane face
Curved edge
Nets for building 3-D shapes
We observe that faces of some 3-D objects are 2-D figures and 2-D figures can be identified.
For example:
(i)a cuboid has six rectangular faces
(ii)a cube has six squared faces
(iii)a triangular pyramid has 4 triangular faces
(iv)a cylinder has 2 circular faces
(v)a cone has 1 circular face.
We will now try to see how some of 3-D objects can be visualized on a 2-D surface i.e. on a
paper. In order to do this, we need to learn more about them by converting these objects into their
nets.
Nets of 3-D shapes
A net is a sort of skeleton – outline in 2-D, which on folding results in a 3-D shape.
To understand this, perform the following activity:
Activity
17
To get a net of a cuboid
Steps
1. Take a cardboard box (as shown in fig. (i)).
2. Cut out some edges to lay the box flat (as shown in fig. (ii)).
(i)
(ii)
Thus, we get a net of a cuboid by suitably cutting the edges. Note that a net of a 3-D object is
a 2-D shape cut from a cardboard or thick paper which on folding forms a 3-D shape.
Visualising Solid Shapes
Different 3-D objects have different nets.
Moreover, net of a 3-D shape may not
be unique.
The adjoining figure shows an open cone.
We can get a net for a cone by cutting a
slit along its slant surface.
We give below nets of some 3-D
objects:
(i)Net for a cube
(ii)Net for a triangular prism
(iii)Net for a pentagonal prism
(iv)Net for a triangular pyramid (tetrahedron)
(v)Net for a square pyramid
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O
Cone
O
Net
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(vi) Net for a cylinder
(vii) Net for a cone
exercise 15.1
1. Match the following shapes with their names:
(i)
(a) Cone
(ii)
(b) cube
(iii)
(c) Prism
(iv)
(d) Sphere
(v)
(e) Cylinder
(vi)
(f) Pyramid
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2. Identify the nets which can be folded to form a cube (cut out copies of the nets and try
it):
(i)
(ii)
(iv)
(iii)
(v)
(vi)
3. Dice are cubes with dots on each face. Opposite faces of a die always
have a total of seven dots on them.
Here are two nets to make dice (cubes); the numbers inserted in each
square indicate the number of dots in that box.
1
4
2
3
5
6
(i)
(ii)
Insert suitable numbers in the blanks, remembering that the number on the opposite faces
should total to 7.
4. Can any of the following be a net for a die? If no, explain your answer:
2
3
1
4
1
2
3
6
4
5
5
(i)
6
(ii)
5. Here is an incomplete net for making a cube. Complete it in atleast two
different ways. Remember that a cube has six faces. How many are there
in the net here?
(You may use a squared paper for easy manipulation.)