Textbook: Three Dimensional Shapes | Mathematics Class 6 (Maharashtra Board) PDF Download

 Page 1


93
Cuboids or Rectangular Prisms
Rectangular Prisms
 
 
All the faces of a cuboid are rectangular and its 
opposite faces are identical or congruent. The cuboid  is 
also a quadrangular prism. How many edges does the 
cuboid have? How many vertices does it have? How 
many faces does it have?
  In the figure here, points A and B are two of the 
eight vertices. Seg AB and seg AP are the names of two 
edges and ABCD is the name of one face.
A cuboid has 12 edges, 8 vertices and 6 faces.
Cubes
 There is a dice in the figure alongside. What difference do you 
see in the shape of a dice and that of a cuboid? When all the faces 
of a quadrangular prism are equal squares, it is called a cube.  
l How many faces does a cube have?
l How many edges does a cube have?
l How many vertices does a cube have?
18 Three Dimensional Shapes
You have learnt to make a 
cuboid from its net. 
Give examples of how the 
same shape can be obtained 
in other ways.
 net shape
A
B
C
P
Q
R
S
D
Let’s recall.
Let’s learn.
Page 2


93
Cuboids or Rectangular Prisms
Rectangular Prisms
 
 
All the faces of a cuboid are rectangular and its 
opposite faces are identical or congruent. The cuboid  is 
also a quadrangular prism. How many edges does the 
cuboid have? How many vertices does it have? How 
many faces does it have?
  In the figure here, points A and B are two of the 
eight vertices. Seg AB and seg AP are the names of two 
edges and ABCD is the name of one face.
A cuboid has 12 edges, 8 vertices and 6 faces.
Cubes
 There is a dice in the figure alongside. What difference do you 
see in the shape of a dice and that of a cuboid? When all the faces 
of a quadrangular prism are equal squares, it is called a cube.  
l How many faces does a cube have?
l How many edges does a cube have?
l How many vertices does a cube have?
18 Three Dimensional Shapes
You have learnt to make a 
cuboid from its net. 
Give examples of how the 
same shape can be obtained 
in other ways.
 net shape
A
B
C
P
Q
R
S
D
Let’s recall.
Let’s learn.
94
Triangular Prisms
 What is the shape of the faces at the base and at 
the top of the figure alongside? 
What is the shape of the faces on the sides? 
Such a figure is called a triangular prism.
How many edges, vertices and faces does a  
triangular prism have?
 Cylinders
 You must have seen a tall box with a circular base. A tin like 
this is a familiar example of a cylinder. If the tin is closed, it is a 
closed cylinder. A closed cylinder has two flat circular faces and one 
curved  face. The cylinder has two circular edges and no vertex.   
Give some examples of cylinders you are familiar with.
    Activity : l 	Take a   l Bring together its l A hollow cylinder
   rectangular sheet. opposite sides. will be formed.
Activity : Take a cylindrical tin. Take a 
rectangular sheet with one side 
equal to the height of the tin. 
Wrap it around the tin to cover it 
completely and cut away the extra 
paper. Then unfold it and spread it 
out on a table. 
Take another sheet. Place the box on it and draw its circular outline. Cut 
away the paper around it. Cut out another circle like this one. Place these 
discs next to the rectangular paper as shown in the figure above. The figure 
obtained is the net of the closed cylinder. Make a cylinder using this net.
Circular
face
Circular 
edge
Curved 
face
A B
C D
A B
D C
AB
DC
net shape 
Try this.
Page 3


93
Cuboids or Rectangular Prisms
Rectangular Prisms
 
 
All the faces of a cuboid are rectangular and its 
opposite faces are identical or congruent. The cuboid  is 
also a quadrangular prism. How many edges does the 
cuboid have? How many vertices does it have? How 
many faces does it have?
  In the figure here, points A and B are two of the 
eight vertices. Seg AB and seg AP are the names of two 
edges and ABCD is the name of one face.
A cuboid has 12 edges, 8 vertices and 6 faces.
Cubes
 There is a dice in the figure alongside. What difference do you 
see in the shape of a dice and that of a cuboid? When all the faces 
of a quadrangular prism are equal squares, it is called a cube.  
l How many faces does a cube have?
l How many edges does a cube have?
l How many vertices does a cube have?
18 Three Dimensional Shapes
You have learnt to make a 
cuboid from its net. 
Give examples of how the 
same shape can be obtained 
in other ways.
 net shape
A
B
C
P
Q
R
S
D
Let’s recall.
Let’s learn.
94
Triangular Prisms
 What is the shape of the faces at the base and at 
the top of the figure alongside? 
What is the shape of the faces on the sides? 
Such a figure is called a triangular prism.
How many edges, vertices and faces does a  
triangular prism have?
 Cylinders
 You must have seen a tall box with a circular base. A tin like 
this is a familiar example of a cylinder. If the tin is closed, it is a 
closed cylinder. A closed cylinder has two flat circular faces and one 
curved  face. The cylinder has two circular edges and no vertex.   
Give some examples of cylinders you are familiar with.
    Activity : l 	Take a   l Bring together its l A hollow cylinder
   rectangular sheet. opposite sides. will be formed.
Activity : Take a cylindrical tin. Take a 
rectangular sheet with one side 
equal to the height of the tin. 
Wrap it around the tin to cover it 
completely and cut away the extra 
paper. Then unfold it and spread it 
out on a table. 
Take another sheet. Place the box on it and draw its circular outline. Cut 
away the paper around it. Cut out another circle like this one. Place these 
discs next to the rectangular paper as shown in the figure above. The figure 
obtained is the net of the closed cylinder. Make a cylinder using this net.
Circular
face
Circular 
edge
Curved 
face
A B
C D
A B
D C
AB
DC
net shape 
Try this.
95
 When playing carrom, you make a pile of the pieces as 
shown in the picture. What is the shape of this pile?  
 If you place a number of CD’s or round biscuits one on top 
of the other, what shape do you get? 
Pyramids
Activity : A net is shown here. It has identical 
triangular sides. Draw a figure like this on 
a card-sheet and cut it out. Fold along the 
dotted lines of the square and bring the 
sides together so that the vertices A, B, C 
and D meet at a point. 
You will get a shape like the one shown 
below. Its base is a square and its other 
standing faces are triangles. 
 This shape is called a pyramid. The top 
or apex of this shape is pointed like a needle. 
As the base of this shape is a quadrilateral, it 
is called a quadrangular pyramid. Count the 
edges, vertices and faces of this shape. 
 A quadrangular pyramid has 5 faces, 8 edges 
and 5 vertices. 
Activity : Draw the net shown alongside on 
a card-sheet and cut it out. Fold 
along the dotted lines of the triangle 
in the centre and bring together the 
triangles on the sides so that the 
vertices A, B and C meet at a point. 
You will get a pyramid. The base 
of this pyramid is a triangle. Hence, 
it is called a triangular pyramid. 
Count and write the number of its 
edges, vertices and faces.
A
B
C
D
vertex
edge
face
Quadrangular Pyramid
A
B
C
Triangular  Pyramid
Try this.
Can you tell?
Page 4


93
Cuboids or Rectangular Prisms
Rectangular Prisms
 
 
All the faces of a cuboid are rectangular and its 
opposite faces are identical or congruent. The cuboid  is 
also a quadrangular prism. How many edges does the 
cuboid have? How many vertices does it have? How 
many faces does it have?
  In the figure here, points A and B are two of the 
eight vertices. Seg AB and seg AP are the names of two 
edges and ABCD is the name of one face.
A cuboid has 12 edges, 8 vertices and 6 faces.
Cubes
 There is a dice in the figure alongside. What difference do you 
see in the shape of a dice and that of a cuboid? When all the faces 
of a quadrangular prism are equal squares, it is called a cube.  
l How many faces does a cube have?
l How many edges does a cube have?
l How many vertices does a cube have?
18 Three Dimensional Shapes
You have learnt to make a 
cuboid from its net. 
Give examples of how the 
same shape can be obtained 
in other ways.
 net shape
A
B
C
P
Q
R
S
D
Let’s recall.
Let’s learn.
94
Triangular Prisms
 What is the shape of the faces at the base and at 
the top of the figure alongside? 
What is the shape of the faces on the sides? 
Such a figure is called a triangular prism.
How many edges, vertices and faces does a  
triangular prism have?
 Cylinders
 You must have seen a tall box with a circular base. A tin like 
this is a familiar example of a cylinder. If the tin is closed, it is a 
closed cylinder. A closed cylinder has two flat circular faces and one 
curved  face. The cylinder has two circular edges and no vertex.   
Give some examples of cylinders you are familiar with.
    Activity : l 	Take a   l Bring together its l A hollow cylinder
   rectangular sheet. opposite sides. will be formed.
Activity : Take a cylindrical tin. Take a 
rectangular sheet with one side 
equal to the height of the tin. 
Wrap it around the tin to cover it 
completely and cut away the extra 
paper. Then unfold it and spread it 
out on a table. 
Take another sheet. Place the box on it and draw its circular outline. Cut 
away the paper around it. Cut out another circle like this one. Place these 
discs next to the rectangular paper as shown in the figure above. The figure 
obtained is the net of the closed cylinder. Make a cylinder using this net.
Circular
face
Circular 
edge
Curved 
face
A B
C D
A B
D C
AB
DC
net shape 
Try this.
95
 When playing carrom, you make a pile of the pieces as 
shown in the picture. What is the shape of this pile?  
 If you place a number of CD’s or round biscuits one on top 
of the other, what shape do you get? 
Pyramids
Activity : A net is shown here. It has identical 
triangular sides. Draw a figure like this on 
a card-sheet and cut it out. Fold along the 
dotted lines of the square and bring the 
sides together so that the vertices A, B, C 
and D meet at a point. 
You will get a shape like the one shown 
below. Its base is a square and its other 
standing faces are triangles. 
 This shape is called a pyramid. The top 
or apex of this shape is pointed like a needle. 
As the base of this shape is a quadrilateral, it 
is called a quadrangular pyramid. Count the 
edges, vertices and faces of this shape. 
 A quadrangular pyramid has 5 faces, 8 edges 
and 5 vertices. 
Activity : Draw the net shown alongside on 
a card-sheet and cut it out. Fold 
along the dotted lines of the triangle 
in the centre and bring together the 
triangles on the sides so that the 
vertices A, B and C meet at a point. 
You will get a pyramid. The base 
of this pyramid is a triangle. Hence, 
it is called a triangular pyramid. 
Count and write the number of its 
edges, vertices and faces.
A
B
C
D
vertex
edge
face
Quadrangular Pyramid
A
B
C
Triangular  Pyramid
Try this.
Can you tell?
96
The top and the bottom faces of a prism are identical. The other faces of triangular, 
quadrangular, etc. prisms are rectangular. 
The standing faces of a pyramid are triangular. 
The name of a prism or a pyramid depends upon the shape of its base.
Cones
You are familiar with examples of cones.
You can see two of them in the pictures below. 
 The tip of the cone is called its apex. 
A cone that is closed by a flat disc has one 
curved face, one circular flat face and one 
circular edge.         
 An open cone has a curved face and a 
circular edge, but no flat face.         
Apex
Curved face
Circular flat face 
Circular edge
This cone has been 
closed after filling it with 
ice
- cream. Its circular top 
is closed.
This is a clown’s cap. 
The circular base of 
this cap is not closed. 
l
Using a compass,
l
	
Draw two radii
l
Cut out the circle.
l
Bring together
draw a circle of the circle,
l
Cut along the the sides
with centre C CR and CS. radii and obtain two CR and CS
on a paper. pieces of the circle. of each piece.
On completing the activity, what shapes did you get?
Try this.
C C
R S
C
R S
C
R S
l l
Now I know -
Page 5


93
Cuboids or Rectangular Prisms
Rectangular Prisms
 
 
All the faces of a cuboid are rectangular and its 
opposite faces are identical or congruent. The cuboid  is 
also a quadrangular prism. How many edges does the 
cuboid have? How many vertices does it have? How 
many faces does it have?
  In the figure here, points A and B are two of the 
eight vertices. Seg AB and seg AP are the names of two 
edges and ABCD is the name of one face.
A cuboid has 12 edges, 8 vertices and 6 faces.
Cubes
 There is a dice in the figure alongside. What difference do you 
see in the shape of a dice and that of a cuboid? When all the faces 
of a quadrangular prism are equal squares, it is called a cube.  
l How many faces does a cube have?
l How many edges does a cube have?
l How many vertices does a cube have?
18 Three Dimensional Shapes
You have learnt to make a 
cuboid from its net. 
Give examples of how the 
same shape can be obtained 
in other ways.
 net shape
A
B
C
P
Q
R
S
D
Let’s recall.
Let’s learn.
94
Triangular Prisms
 What is the shape of the faces at the base and at 
the top of the figure alongside? 
What is the shape of the faces on the sides? 
Such a figure is called a triangular prism.
How many edges, vertices and faces does a  
triangular prism have?
 Cylinders
 You must have seen a tall box with a circular base. A tin like 
this is a familiar example of a cylinder. If the tin is closed, it is a 
closed cylinder. A closed cylinder has two flat circular faces and one 
curved  face. The cylinder has two circular edges and no vertex.   
Give some examples of cylinders you are familiar with.
    Activity : l 	Take a   l Bring together its l A hollow cylinder
   rectangular sheet. opposite sides. will be formed.
Activity : Take a cylindrical tin. Take a 
rectangular sheet with one side 
equal to the height of the tin. 
Wrap it around the tin to cover it 
completely and cut away the extra 
paper. Then unfold it and spread it 
out on a table. 
Take another sheet. Place the box on it and draw its circular outline. Cut 
away the paper around it. Cut out another circle like this one. Place these 
discs next to the rectangular paper as shown in the figure above. The figure 
obtained is the net of the closed cylinder. Make a cylinder using this net.
Circular
face
Circular 
edge
Curved 
face
A B
C D
A B
D C
AB
DC
net shape 
Try this.
95
 When playing carrom, you make a pile of the pieces as 
shown in the picture. What is the shape of this pile?  
 If you place a number of CD’s or round biscuits one on top 
of the other, what shape do you get? 
Pyramids
Activity : A net is shown here. It has identical 
triangular sides. Draw a figure like this on 
a card-sheet and cut it out. Fold along the 
dotted lines of the square and bring the 
sides together so that the vertices A, B, C 
and D meet at a point. 
You will get a shape like the one shown 
below. Its base is a square and its other 
standing faces are triangles. 
 This shape is called a pyramid. The top 
or apex of this shape is pointed like a needle. 
As the base of this shape is a quadrilateral, it 
is called a quadrangular pyramid. Count the 
edges, vertices and faces of this shape. 
 A quadrangular pyramid has 5 faces, 8 edges 
and 5 vertices. 
Activity : Draw the net shown alongside on 
a card-sheet and cut it out. Fold 
along the dotted lines of the triangle 
in the centre and bring together the 
triangles on the sides so that the 
vertices A, B and C meet at a point. 
You will get a pyramid. The base 
of this pyramid is a triangle. Hence, 
it is called a triangular pyramid. 
Count and write the number of its 
edges, vertices and faces.
A
B
C
D
vertex
edge
face
Quadrangular Pyramid
A
B
C
Triangular  Pyramid
Try this.
Can you tell?
96
The top and the bottom faces of a prism are identical. The other faces of triangular, 
quadrangular, etc. prisms are rectangular. 
The standing faces of a pyramid are triangular. 
The name of a prism or a pyramid depends upon the shape of its base.
Cones
You are familiar with examples of cones.
You can see two of them in the pictures below. 
 The tip of the cone is called its apex. 
A cone that is closed by a flat disc has one 
curved face, one circular flat face and one 
circular edge.         
 An open cone has a curved face and a 
circular edge, but no flat face.         
Apex
Curved face
Circular flat face 
Circular edge
This cone has been 
closed after filling it with 
ice
- cream. Its circular top 
is closed.
This is a clown’s cap. 
The circular base of 
this cap is not closed. 
l
Using a compass,
l
	
Draw two radii
l
Cut out the circle.
l
Bring together
draw a circle of the circle,
l
Cut along the the sides
with centre C CR and CS. radii and obtain two CR and CS
on a paper. pieces of the circle. of each piece.
On completing the activity, what shapes did you get?
Try this.
C C
R S
C
R S
C
R S
l l
Now I know -
97
Spheres
The shape of a laddoo, a ball, 
a shot put is called a sphere. 
The sphere has just one curved face. 
It does not have any vertices or edges.
??	 Write the number of faces, edges and vertices of each shape in the table. 
Name Cylinder  Cone
Pentagonal
pyramid 
Hexagonal
pyramid 
Hexagonal
prism
Pentagonal
prism
Shape
Faces
Vertices
Edges
?????? Practice Set 41