RS Aggarwal Solutions: Three-Dimensional Shapes | Mathematics (Maths) Class 6 PDF Download

 Page 1


Points to Remember :
1. Solid. An object that has a fixed shape
and size is caled a solid. A solid occupies
a fixed amount of space.
Solids occur in different shapes.
These shapes are known as three-
dimensional shapes.
The various types of these shapes are
shown below.
2. Cuboid. Solids such as a wooden box, a
matchbox, a brick, a book, an almirah,
etc., are all in the shape of a cuboid.
Some of these shapes are given below.
A cuboid has length, breadth and height.
Various parts of a cuboid are given below :
(i) Faces. A cuboid has six rectangular faces.
The opposite faces of a cuboid are
identical.
(ii) Edges. Two adjacent faces of a cuboid
meet in a line segment, called an edge of
the cuboid. A cuboid has 12 edges.
(iii) Vertices. Three edges of a cuboid meet
at a point, called a vertex. A cuboid has 8
vertices.
Thus, a cuboid has 6 rectangular faces,
12 edges and 8 vertices.
3. Cube. A cuboid whose length, breadth
and height are equal is called a cube.
Page 2


Points to Remember :
1. Solid. An object that has a fixed shape
and size is caled a solid. A solid occupies
a fixed amount of space.
Solids occur in different shapes.
These shapes are known as three-
dimensional shapes.
The various types of these shapes are
shown below.
2. Cuboid. Solids such as a wooden box, a
matchbox, a brick, a book, an almirah,
etc., are all in the shape of a cuboid.
Some of these shapes are given below.
A cuboid has length, breadth and height.
Various parts of a cuboid are given below :
(i) Faces. A cuboid has six rectangular faces.
The opposite faces of a cuboid are
identical.
(ii) Edges. Two adjacent faces of a cuboid
meet in a line segment, called an edge of
the cuboid. A cuboid has 12 edges.
(iii) Vertices. Three edges of a cuboid meet
at a point, called a vertex. A cuboid has 8
vertices.
Thus, a cuboid has 6 rectangular faces,
12 edges and 8 vertices.
3. Cube. A cuboid whose length, breadth
and height are equal is called a cube.
Examples. Ice cubes, sugar cubes, dice,
etc., are all examples of a cube.
Clearly, a cube like cuboid has 6 square
faces, 12 edges and 8 vertices.
4. Cylinder. Objects such as a circular
pillar ; a circular pipe, a test tube, a
circular storage tank, a measuring jar ; a
gas cylinder, a circular powder tin, etc.,
are in the shape of a cylinder.
Some of these shapes are shown below.
A cylinder has a curved lateral surface
and two circular faces at its ends.
A cylinder has no corner or vertex.
A cylinder has two plane faces, namely
the top and the base, and one curved face.
It has 2 circular edges.
The distance between its ends faces is
called its length.
5. Cone. Objects such as an ice-cream cone,
a conical tent, a conical vessel, a clown’ s
cap, etc., are in the shape of a cone.
Some examples of cones are given below.
A cone has a plane circular end as the
base and a curved surface tapering into a
point, called its vertex.
Thus, a cone has one plane face (i.e.
base) and one curved face.
It has one circular edge and one vertex.
6. Sphere. An object which is in the shape
of a ball is said to have the shape of a
sphere.
A sphere has a curved surface.
A sphere has no vertex and no edge.
Page 3


Points to Remember :
1. Solid. An object that has a fixed shape
and size is caled a solid. A solid occupies
a fixed amount of space.
Solids occur in different shapes.
These shapes are known as three-
dimensional shapes.
The various types of these shapes are
shown below.
2. Cuboid. Solids such as a wooden box, a
matchbox, a brick, a book, an almirah,
etc., are all in the shape of a cuboid.
Some of these shapes are given below.
A cuboid has length, breadth and height.
Various parts of a cuboid are given below :
(i) Faces. A cuboid has six rectangular faces.
The opposite faces of a cuboid are
identical.
(ii) Edges. Two adjacent faces of a cuboid
meet in a line segment, called an edge of
the cuboid. A cuboid has 12 edges.
(iii) Vertices. Three edges of a cuboid meet
at a point, called a vertex. A cuboid has 8
vertices.
Thus, a cuboid has 6 rectangular faces,
12 edges and 8 vertices.
3. Cube. A cuboid whose length, breadth
and height are equal is called a cube.
Examples. Ice cubes, sugar cubes, dice,
etc., are all examples of a cube.
Clearly, a cube like cuboid has 6 square
faces, 12 edges and 8 vertices.
4. Cylinder. Objects such as a circular
pillar ; a circular pipe, a test tube, a
circular storage tank, a measuring jar ; a
gas cylinder, a circular powder tin, etc.,
are in the shape of a cylinder.
Some of these shapes are shown below.
A cylinder has a curved lateral surface
and two circular faces at its ends.
A cylinder has no corner or vertex.
A cylinder has two plane faces, namely
the top and the base, and one curved face.
It has 2 circular edges.
The distance between its ends faces is
called its length.
5. Cone. Objects such as an ice-cream cone,
a conical tent, a conical vessel, a clown’ s
cap, etc., are in the shape of a cone.
Some examples of cones are given below.
A cone has a plane circular end as the
base and a curved surface tapering into a
point, called its vertex.
Thus, a cone has one plane face (i.e.
base) and one curved face.
It has one circular edge and one vertex.
6. Sphere. An object which is in the shape
of a ball is said to have the shape of a
sphere.
A sphere has a curved surface.
A sphere has no vertex and no edge.
7. Triangular prism. A solid whose lateral
faces are rectangular and the bases are
congruent triangles, is called a triangular
prism.
The adjoining figure shows a triangular
prism, denoted by (ABC, PQR).
A triangular prism has 6 vertices, 3
rectangular lateral faces, 2 triangular bases
and 9 edges.
8. Pyramid. A pyramid is a solid whose base
is a plane rectilinear figure and whose side
faces are triangles having a common
vertex, called the vertex of the pyramid.
The length of perpendicular drawn from
the vertex of a pyramid to its base is called
the height of the pyramid.
The side faces of a pyramid are called its
lateral faces.
(i) Square pyramid. A solid whose base is
a square and whose side faces are triangles
having a common vertex is called a square
pyramid.
The adjacent figure shows a square
pyramid OABCD with O as vertex, the
square ABCD as its base and OP as its
height.
A square pyramid has 4 lateral triangular
faces and 8 edges.
(ii) Triangular pyramid. A solid whose base
is a triangle and whose side faces are
triangles having a common vertex is called
a triangular pyramid.
The adjacent figure shows a triangular
pyramid OABC with O as vertex and
ABC as its base.
A triangular pyramid has 3 triangular lateral
faces, one triangular base and 6 edges.
A triangular pyramid is also called a
tetrahedron.
          Tick ( ) the correct answer in each of
Q. 1 to Q. 6.
Q. 1. A cuboid has
(a) length only
(b) length and breadth only
(c) length, breadth and height
(d) thickness only
Q. 2. A dice is an example of a
(a) cuboid  (b) cube  (c) cone  (d) cylinder
Q. 3. A gas pipe is an example of a
(a) cuboid  (b) cube  (c) cone  (d) cylinder
Q. 4. A football is an example of a
(a) cylinder (b) cone (c) sphere (d) none of these
Q. 5 A brick is an example of a
(a) cube  (b) cuboid  (c) prism  (d) cylinder
Q. 6. An ice-cone is an example of a
(a) cuboid  (b) cube (c) pyramid (d) none of these
Sol. 1. (c) 
.
.
.
 A cuboid has three dimensions,
length, breadth and height or depth.
2. (b) 
.
.
.
 Its six faces arc of square.
3. (d) 
.
.
.
 Its shape is of a cylinder as it is
round in shape on either sides/faces.
Page 4


Points to Remember :
1. Solid. An object that has a fixed shape
and size is caled a solid. A solid occupies
a fixed amount of space.
Solids occur in different shapes.
These shapes are known as three-
dimensional shapes.
The various types of these shapes are
shown below.
2. Cuboid. Solids such as a wooden box, a
matchbox, a brick, a book, an almirah,
etc., are all in the shape of a cuboid.
Some of these shapes are given below.
A cuboid has length, breadth and height.
Various parts of a cuboid are given below :
(i) Faces. A cuboid has six rectangular faces.
The opposite faces of a cuboid are
identical.
(ii) Edges. Two adjacent faces of a cuboid
meet in a line segment, called an edge of
the cuboid. A cuboid has 12 edges.
(iii) Vertices. Three edges of a cuboid meet
at a point, called a vertex. A cuboid has 8
vertices.
Thus, a cuboid has 6 rectangular faces,
12 edges and 8 vertices.
3. Cube. A cuboid whose length, breadth
and height are equal is called a cube.
Examples. Ice cubes, sugar cubes, dice,
etc., are all examples of a cube.
Clearly, a cube like cuboid has 6 square
faces, 12 edges and 8 vertices.
4. Cylinder. Objects such as a circular
pillar ; a circular pipe, a test tube, a
circular storage tank, a measuring jar ; a
gas cylinder, a circular powder tin, etc.,
are in the shape of a cylinder.
Some of these shapes are shown below.
A cylinder has a curved lateral surface
and two circular faces at its ends.
A cylinder has no corner or vertex.
A cylinder has two plane faces, namely
the top and the base, and one curved face.
It has 2 circular edges.
The distance between its ends faces is
called its length.
5. Cone. Objects such as an ice-cream cone,
a conical tent, a conical vessel, a clown’ s
cap, etc., are in the shape of a cone.
Some examples of cones are given below.
A cone has a plane circular end as the
base and a curved surface tapering into a
point, called its vertex.
Thus, a cone has one plane face (i.e.
base) and one curved face.
It has one circular edge and one vertex.
6. Sphere. An object which is in the shape
of a ball is said to have the shape of a
sphere.
A sphere has a curved surface.
A sphere has no vertex and no edge.
7. Triangular prism. A solid whose lateral
faces are rectangular and the bases are
congruent triangles, is called a triangular
prism.
The adjoining figure shows a triangular
prism, denoted by (ABC, PQR).
A triangular prism has 6 vertices, 3
rectangular lateral faces, 2 triangular bases
and 9 edges.
8. Pyramid. A pyramid is a solid whose base
is a plane rectilinear figure and whose side
faces are triangles having a common
vertex, called the vertex of the pyramid.
The length of perpendicular drawn from
the vertex of a pyramid to its base is called
the height of the pyramid.
The side faces of a pyramid are called its
lateral faces.
(i) Square pyramid. A solid whose base is
a square and whose side faces are triangles
having a common vertex is called a square
pyramid.
The adjacent figure shows a square
pyramid OABCD with O as vertex, the
square ABCD as its base and OP as its
height.
A square pyramid has 4 lateral triangular
faces and 8 edges.
(ii) Triangular pyramid. A solid whose base
is a triangle and whose side faces are
triangles having a common vertex is called
a triangular pyramid.
The adjacent figure shows a triangular
pyramid OABC with O as vertex and
ABC as its base.
A triangular pyramid has 3 triangular lateral
faces, one triangular base and 6 edges.
A triangular pyramid is also called a
tetrahedron.
          Tick ( ) the correct answer in each of
Q. 1 to Q. 6.
Q. 1. A cuboid has
(a) length only
(b) length and breadth only
(c) length, breadth and height
(d) thickness only
Q. 2. A dice is an example of a
(a) cuboid  (b) cube  (c) cone  (d) cylinder
Q. 3. A gas pipe is an example of a
(a) cuboid  (b) cube  (c) cone  (d) cylinder
Q. 4. A football is an example of a
(a) cylinder (b) cone (c) sphere (d) none of these
Q. 5 A brick is an example of a
(a) cube  (b) cuboid  (c) prism  (d) cylinder
Q. 6. An ice-cone is an example of a
(a) cuboid  (b) cube (c) pyramid (d) none of these
Sol. 1. (c) 
.
.
.
 A cuboid has three dimensions,
length, breadth and height or depth.
2. (b) 
.
.
.
 Its six faces arc of square.
3. (d) 
.
.
.
 Its shape is of a cylinder as it is
round in shape on either sides/faces.
4. (c) 
.
.
.
 Football is round as sphere.
5. (b) 
.
.
.
 A brick has length, breadth and height.
6. (d) 
.
.
.
 Its shape is like a cone.  Ans.
Q. 7. Fill in the blanks :
(i) An object that occupies space is called a..... .
(ii) A cuboid has........faces, .........edges and.........vertices.
(iii) The.........faces of a cuboid are identical.
(iv) A............has no vertex and no edge.
(v) All the faces of a............are identical.
(vi) A square pyramid has............lateral triangular faces and............edges.
(vii) A triangular pyramid has........triangular lateral faces and............edges.
(viii) A triangular prism has..........vertices, ..........rectangular lateral faces, ..........triangular bases
and.........edges.
Sol. (i) solid (ii) 6, 12 and 18 (iii) opposite
(iv) sphere (v) cube (vi) 4, 8
(vii) 3, 6 (viii) 6, 3, 2, 9   Ans.
Q. 8. Give examples of four objects which are in the shape of :
(a) a cone (b) a cuboid (c) a cylinder.
Sol. (a) A cone:
(i) Conical cup (ii) An ice cream cup
(iii) Conical tent house (iv) Conical vessel.
(b) A cuboid :
(i) A book, (ii) A brick,
(iii) a box, (iv) a brief case.
(c) A cylinder :
(i) Circular pipe (ii) A jar or tumbler
(iii) A round powder tin (iv) Circular piller.