1. Revision
Description
Recall basics of
solid.
Reflect and Review


The point of
intersection of two lines
is a point.
The surface of any solid
is a 2-D figure.
Teasers
1) How many circles
does the net of cone
have?
2) The intersection of
two planes is a
______.
2. Views of 3-D shapes
Description
Reflect and Review
A 3-D object may
look different from
different positions.
View of a 3-D shape
is what you see
while observing the
object from
different positions.
The different views
are:
• Front view
• Top view
• Side view
Teasers
1) Draw the top,
front and side
views of the
below figure.
Answers
1) 1
2) Line
segment
Answers
1) Top view
Front view
The front, top and side views of
the above figure is as follows
Front view
Side view
1
Top view
Side view
3. Polyhedrons
Description

2
A three-dimensional solid composed of
polygons is called a polyhedron.
- Faces: The polygons forming a polyhedron.
- Edges: The line segments formed by
intersection of the faces of a polyhedron.
- Vertices: The corners where the edges of a
polyhedron intersect or the point where
three or more edges meet.
Reflect and
Review
Example of concave
polyhedron
Teasers
Answers
1) Give an
1) Pencil box
example 2)
of convex
polyhedr
on.
2) Give an
example
of
concave
polyhedr
on
.

Some of the non- polyhedron solids are
cylinder, cone and sphere.

Convex and Concave Polyhedron:
If in any polyhedron, the line segment joining
any two points on its surface lie entirely inside
or on the polyhedron, then the polyhedron is
called a convex polyhedron. Otherwise, it is a
concave polyhedron.
Cube, cuboid, pyramid and prism are the
examples of convex polyhedrons.

Regular Polyhedron:
If the faces of a polyhedron are regular
polygons and the same number of faces meet at
each vertex, then the polyhedron is called a
regular polyhedron. E.g., cube.
4. Platonic solids
Description


A platonic solid is a regular, convex
polyhedron. There are only 5 platonic
solids. In a platonic solid,
i. All edges are of equal length.
ii. All angles are of equal measure.
iii. All faces are congruent.
The five platonic solids are:
Tetrahedron: It is also called triangular
pyramid. Its faces are congruent
Reflect and Review


Another name of a cube
is hexahedron.
The number of
equilateral faces in a
icosahedron is 10.
Teasers
1) What is
another name
for a
triangular
pyramid?
2) How many
equilateral
triangles meet
at each vertex
of an
Answers
1) Tetrahedron
2) 4
3
equilateral triangles.
octahedron
has?
Hexahedron: It is also called cube. Its
faces are squares.
Octahedron: It has 4 equilateral
triangles meeting at each vertex.
Icosahedron: It has 5 equilateral
triangles meeting at each vertex.
Dodecahedron: It has 3 pentagons
meeting at each vertex.
5. Euler’s formula
Description
The Euler’s formula states that the number
of faces (F), the number of vertices (V) and
the number of edges (E) of a simple convex
polyhedron maintain a relationship:
F+V=E+2
Name of
Platonic
Solid
4
Numb
er of
Faces
(F)
Numb
er of
Vertice
s (V)
Numb
er of
Edges
(E)
Reflect and
Review
Teasers
Answers
If number of
faces, F = 7 and
number of edges,
E = 12, then to
find the number
of vertices, V:
1) Using Euler’s formula,
find the missing values.
1) E = 24; F =
11; V = 4
Using Euler’s
formula, we can
write
7 + V = 12 + 2
Faces
Vertices
Edges
10
16
4
11
20
6
Tetrahedron
Hexahedron
(Cube)
Octahedron
Icosahedron
Dodecahedr
on
4
6
4
8
6
12
8
20
12
6
12
20
12
30
30
i.e., V = 7.
6. Prisms and Pyramids
Description
Prism
A prism is a polyhedron for which the top and
bottom faces (known as bases) are congruent
polygons and all other faces (lateral faces) are
parallelograms.
Pyramid
A pyramid is a polyhedron whose base is a polygon
and whose lateral faces are triangles having a
common vertex.
Reflect and
Review

The lateral face
of a prism is a
parallelogram.

The lateral face
of a pyramid is
a triangle.
Teasers
Answers
Find the number 1) 5
of lateral faces
2) 3
of the following
1) Pentagonal
prism
2) Triangular
pyramid
5
7. Combination of solids or nested solids
Description
The objects formed by combining two solid figures
or by nesting solid within each other are called
nested objects.
Examples:
 Funnel – A combination of a cone and cylinder
 Ice cream cone – A combination of cone and
hemisphere.
Reflect and
Review
Teasers
Examples of nested
objects:
 A combination
of cube and
cylinder.
1) Give an
example
of nested
solids.
Answers
1)
A combination of
cone and cylinder.

8. Visualisation of 3-D Shapes through Nets
Description


6
A net for a 3-D shape is a basic structure in two
dimensions, which when folded regains the 3-D
shape.
This tool helps in visualising 3-D shapes more
clearly.
A combination
of cylinder and
cone.
Reflect and
Review
Teasers
Answers
The net of a cone
is as shown
below
1) Which solid
does the net
shown below
represent?
1) Octahe
dron
7