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BOOK 8 ( CBSE ) / Chap10 /Visualizing Solid Shapes
Chapter Facts.
1. A plane figure has two dimensions (2 – D) and a solid figure has three dimensions
( 3 – D ).
2. Some solid shapes consist of one figure embedded in the other ( cylinder with a conical
grove ) or combination of two figures ( cone mounted on a cylinder) . Such solids are
called nested solids.
3. 3D objects have different views (front-view, top – view and side – view)
from different positions.
4. A map is different from a picture. It depicts the location of a particular object/place in
relation to other objects/places. Symbols are used to depict the different objects/places.
5. Maps involve a scale which is fixed for a particular map.
6. Perspective is very important for drawing a picture but is not relevant for a map.
7. The corners of a solid shape are called its vertices; the line segments of its skeleton
are its edges; and its flat surfaces are its faces.
8. A solid all whose faces are polygons is called a polyhedron. Cube , cuboid , prism ,
pyramid are examples of polyhedrons.
9. A solid having a surface which is not a polygon is not a polyhedron. Cone , sphere ,
cylinder are not polyhedrons.
10. A polyhedron is said to be convex if angle between any of its two edges is less than
180o.
11. A polyhedron is said to be concave if at least one angle between any of its two edges
is a reflex angle.
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12. A polyhedron is said to be regular if its faces are made up of regular polygons and
the same number of faces meet at each vertex. A cube is a regular polygon as all faces are
identical. A cuboid is not regular because all faces are not identical.
13. A prism is a solid shape whose base and top are congruent polygons and lateral faces
are parallelograms in shape.
14. A right prism is a solid with congruent polygons on top and bottom and rectangles
on sides. Some prisms are. :
Triangular
Rectangular
prism
prism
Square prism

A cube can be called a square prism.

A cuboid can be called a rectangular prism.
Pentagonal
Hexagonal
prism
prism
14. A pyramid is a solid shape whose base is a polygon and lateral faces are triangles
with common vertex. Some pyramids are :
Triangular pyramid
Square pyramid
Rectangular pyramid
Pentagonal pyramid
Base is a triangle
Base is a square
Base is a pentagon
Base is a rectangle
15. For any polyhedron, F + V – E = 2 where ‘F’ stands for number of faces, V stands for
number of vertices and E stands for number of edges. This relationship is called Euler’s
formula.
Formative Assessment
A ) Multiple Choice Questions
Tick () the correct answer for each of the following :
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1. The other name of a triangular pyramid is
(a) tetrahedron
(b) octahedron
(c) cuboid
(d) cube
2. Four vertices are found in
(a) triangular prism
(b) square pyramid
(c) rectangular pyramid
(d) triangular pyramid
3. Number of edges in a rectangular pyramid is
(a) 7
(b) 8
(c) 9
(d) 12
(c) 5
(d) 7
4. The number of vertices in a triangular prism is
(a) 6
(b) 8
5. How many faces are there in a pyramid whose base is a polygon of 6 sides?
(a) 6
(b) 12
(c) 8
(d) 14
6. How many vertices are there in a prism whose base is a polygon of 5 sides?
(a) 10
(b) 12
(c) 14
(d) 15
B ) Fill in the blanks:
1. A tetrahedron has _____________ faces, _____________ edges and
_____________ vertices.
2. The _____________ are used to depict the object/places in a map.
3. A cube can be called a ___________ prism.
4. Perspective is very important for drawing a _______ but is not relevant for a
_______ .
5. A polyhedron is said to be ___________ if at least one angle between any of its two
edges is a reflex angle.
C) True / False
Say true or false for each of the following.
1. Maps involve a scale which is fixed for a particular map.
T/F
2. 3D objects may have different views from different positions.
T/F
3. A cuboid can be called a rectangular prism.
T/F
4. The distances shown on a map are proportional to the actual distances on the ground.
T/F
D ) True / False with Justification :
Say true or false for each of the following. Justify your answer ?
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1. A cuboid is not a regular polygon.
T/F
______________________________________________________________________
______________________________________________________________________
2. A prism is a solid with congruent polygons on top and bottom and rectangles on sides.
T/F
______________________________________________________________________
______________________________________________________________________
E ) Matching
Match the items in column I with items in column II.
Column I
(i)
Column II
A Concave polyhedron
(ii)
B Hexagonal pyramid
(iii)
C Triangular bi pyramid
(iv)
D Square prism
(v)
E
Pentagonal prism
(vi)
F
Pentagonal Pyramid
G Nested solid
.
Summative Assessment
A ) One mark questions
1. A polyhedron has 10 faces and 5 vertices. Find the number of edges it has.
2. A polyhedron has 12 faces and 18 edges. Find the number of vertices it has.
3. A polyhedron has 7 vertices and 14 edges. Find the number of faces it has.
4. Is it possible to have a polyhedron with 7 faces , 5 vertices and 9 edges ?
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5. Is it possible to have a polyhedron with 9 faces , 6 vertices and 13 edges ?
B ) Two mark questions
1. Draw side and top view for the following
Side view
Top view
2. Draw side and front view for the following
Side view
Front view
3. Draw top and front view for the following
Top view
Front view
C ) Three mark questions
Draw front , side and top view for each of the following
Front view
Side view
Top view
1
2
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Verify the Euler’s formula for each of the following polyhedrons.
3
F = _____ , V = _________ E = _________
Then F + V – E = ____ + ___ + _______ = _______ .
Euler’s formula is : verified / not verified. ( cross out the incorrect
)
F = _____ , V = _________ E = _________
4
Then F + V – E = ____ + ___ + _______ = _______ .
Euler’s formula is : verified / not verified. ( cross out the incorrect
)
F = _____ , V = _________ E = _________
5
Then F + V – E = ____ + ___ + _______ = _______ .
Euler’s formula is : verified / not verified. ( cross out the incorrect
)
F = _____ , V = _________ E = _________
6
Then F + V – E = ____ + ___ + _______ = _______ .
Euler’s formula is : verified / not verified. ( cross out the incorrect
)
F = _____ , V = _________ E = _________
7
Then F + V – E = ____ + ___ + _______ = _______ .
Euler’s formula is : verified / not verified. ( cross out the incorrect
)
D ) Four mark questions
Draw the object whose front , side and top views are given. ( 1-2 )
Front view
Side view
Top view
Object
1
2
End
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