#### Chapters

Chapter 2: Data Handling

Chapter 3: Square-Square Root and Cube-Cube Root

Chapter 4: Linear Equation In One Variable

Chapter 5: Understanding Quadrilaterals and Practical Geometry

Chapter 6: Visualising Solid Shapes

Chapter 7: Algebraic Expression, Identities and Factorisation

Chapter 8: Exponents and Powers

Chapter 9: Comparing Quantities

Chapter 10: Direct and Inverse Proportions

Chapter 11: Mensuration

Chapter 12: Introduct To Graphs

Chapter 13: Playing With Numbers

## Chapter 6: Visualising Solid Shapes

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 6 Visualising Solid Shapes Exercise [Pages 181 - 205]

#### Choose the correct alternative:

Which amongst the following is not a polyhedron?

Which of the following will not form a polyhedron?

3 triangle

2 triangles and 3 parallelogram

8 triangles

1 pentagon and 5 triangles

Which of the following is a regular polyhedron?

Cuboid

Triangular prism

Cube

Square prism

Which of the following is a two Dimensional figure?

Rectangle

Rectangular Prism

Square Pyramid

Square Prism

Which of the following can be the base of a pyramid?

Line segmen

Circle

Octagon

Oval

Which of the following 3D shapes does not have a vertex?

Pyramid

Prism

Cone

Sphere

Solid having only line segments as its edges is a ______.

Polyhedron

Cone

Cylinder

Polygon

In a solid if F = V = 5, then the number of edges in this shape is ______.

6

4

8

2

Which of the following is the top view of the given shape?

The net shown below can be folded into the shape of a cube. The face marked with the letter L is opposite to the face marked with which letter?

M

N

Q

O

Which of the nets given below will generate a cone?

Which of the following is not a prism?

We have 4 congruent equilateral triangles. What do we need more to make a pyramid?

An equilateral triangle

A square with same side length as of triangle

2 equilateral triangles with side length same as triangle

2 squares with side length same as triangle

Side of a square garden is 30 m. If the scale used to draw its picture is 1 cm: 5 m, the perimeter of the square in the picture is ______.

20 cm

24 cm

28 cm

30 cm

Which of the following shapes has a vertex?

In the given map, the distance between the places is shown using the scale 1 cm : 0.5 km. Then the actual distance (in km) between school and the book shop is ______.

1.25

2.5

2

1.1

Which of the following cannot be true for a polyhedron?

V = 4, F = 4, E = 6

V = 6, F = 8, E = 12

V = 20, F = 12, E = 30

V = 4, F = 6, E = 6

In a blueprint of a room, an architect has shown the height of the room as 33 cm. If the actual height of the room is 330 cm, then the scale used by her is ______.

1:11

1:10

1:100

1:3

The following is the map of a town. Based on it answer questions 19 - 21.

The number of hospitals in the town is ______.

1

2

3

4

The ratio of the number of general stores and that of the ground is ______.

1:2

2:1

2:3

3:2

According to the map, the number of schools in the town is ______.

4

3

5

2

#### Fill in the blanks:

Square prism is also called a ______.

Rectangular prism is also called a ______.

In the figure, the number of faces meeting at B is ______.

A pyramid on an n sided polygon has ______ faces.

If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.

The given net can be folded to make a ______.

A solid figure with only 1 vertex is a ______.

Total number of faces in a pyramid which has eight edges is ______.

The net of a rectangular prism has ______ rectangles.

In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the ______ face.

If 4 km on a map is represented by 1 cm, then 16 km is represented by ______ cm.

If actual distance between two places A and B is 110 km and it is represented on a map by 25 mm. Then the scale used is ______.

A pentagonal prism has ______ faces.

If a pyramid has a hexagonal base, then the number of vertices is ______.

is the ______ view of

The number of cubes in are ______

If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.

Total number of regular polyhedra is ______.

A regular polyhedron is a solid made up of ______ faces.

For each of the following solids, identify the front, side and top views and write it in the space provided.

For each of the following solids, identify the front, side and top views and write it in the space provided.

For each of the following solids, identify the front, side and top views and write it in the space provided.

#### State whether the following statement is True or False:

The other name of cuboid is tetrahedron.

True

False

A polyhedron can have 3 faces.

True

False

A polyhedron with least number of faces is known as a triangular pyramid.

True

False

Regular octahedron has 8 congruent faces which are isosceles triangles.

True

False

Pentagonal prism has 5 pentagons.

True

False

Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.

True

False

Euler’s formula is true for all three-dimensional shapes.

True

False

A polyhedron can have 10 faces, 20 edges and 15 vertices.

True

False

The top view of

True

False

The number of edges in a parallelogram is 4.

True

False

Every solid shape has a unique net.

True

False

Pyramids do not have a diagonal.

True

False

The given shape is a cylinder.

True

False

A cuboid has atleast 4 diagonals.

True

False

All cubes are prisms

True

False

A cylinder is a 3-D shape having two circular faces of different radii.

True

False

On the basis of the given figure, the length of a rectangle in the net of a cylinder is same as circumference of circles in its net.

True

False

If a length of 100 m is represented on a map by 1 cm, then the actual distance corresponding to 2 cm is 200 m.

True

False

The model of a ship shown is of height 3.5 cm. The actual height of the ship is 210 cm if the scale chosen is 1: 60.

True

False

The actual width of a storeroom is 280 cm. If the scale chosen to make its drawing is 1:7, then the width of the room in the drawing will be 40 cm.

True

False

Complete the table given below:

S.No |
Solid |
Shape of Solid |
Number of faces F |
Number of Verticles V |
Number of edges E |
F + V |
E + 2 |

a. | Cuboid | ||||||

b. | Triangular Pyramid | ||||||

c. | Square Pyramid | ||||||

d. | Rectangular Pyramid | ||||||

e. | Pentagonal Pyramid | ||||||

f. | Hexagonal Pyramid | ||||||

g. | Triangular Prism | ||||||

h. | Square Prism | ||||||

i. | Cube | ||||||

j. | Pentagonal Prism | ||||||

k. | Octagonal Prism | ||||||

l. | Heptagonal Prism |

How many faces does the following solids, have tetrahedron?

How many faces does the following solids, have hexahedron?

How many faces does the following solids have octagonal pyramid?

How many faces does the following solids have octahedron?

Draw a prism with its base as regular hexagon with one of its face facing you. Now draw the top view, front view and side view of this solid.

How many vertices does the following solids have?

Cone

How many vertices does the following solids have?

Cylinder

How many vertices does the following solids have?

Sphere

How many vertices does the following solids have?

Octagonal Pyramid

How many vertices does the following solids have?

Tetrahedron

How many vertices does the following solids have?

Hexagonal Prism

How many edges does following solids have?

Cone

How many edges does following solids have?

Cylinder

How many edges does following solids have?

Sphere

How many edges does following solids have?

Octagonal Pyramid

How many edges does following solids have?

Hexagonal Prism

How many edges does following solids have?

Kaleidoscope

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Count the number of cubes in the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Draw the front, side and top view of the given shapes.

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
7 |

Vertices |
10 |

Edges |
x |

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
y |

Vertices |
12 |

Edges |
18 |

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
9 |

Vertices |
z |

Edges |
16 |

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
p |

Vertices |
6 |

Edges |
12 |

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
6 |

Vertices |
q |

Edges |
12 |

Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.

Faces |
8 |

Vertices |
11 |

Edges |
r |

Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.

Check whether a polyhedron can have V = 12, E = 6 and F = 8.

A polyhedron has 60 edges and 40 vertices. Find the number of its faces.

Find the number of faces in the given shapes:

Find the number of faces in the given shapes:

Find the number of faces in the given shapes:

A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.

A solid has forty faces and, sixty edges. Find the number of vertices of the solid.

Draw the net of a regular hexahedron with side 3 cm. (Hint: Regular hexahedron - cube)

Draw the net of a regular tetrahedron with side 6 cm.

Draw the net of the following cuboid:

#### Match the following:

Figure |
Name |

(a) | (a) Hexahedron |

(b) | (b) Hexagonal Prism |

(c) | (c) Square Pyramid |

(d) | (d) Cone |

Complete the table given below by putting tick mark across the respective property found in the solids mentioned.

Solids |
||||

Properties |
Cone |
Cylinder |
Prism |
Pyramid |

1. The figure is a Polyhedron | ||||

2. The figure has diagonals | ||||

3. The shape has curved edges | ||||

4. The base of figure is a polygon | ||||

5. The bases are congruent | ||||

6. The base of figure is a polygon and other faces meet at a single point |
||||

7. The base of figure is a curved edge and other faces meet at a single point |

Draw the net of the following shape.

Draw the net of the following solid.

(Hint: Pentagons are not congruent.)

Find the number of cubes in the base layer of the following figure.

In the above figure, if only the shaded cubes are visible from the top, draw the base layer.

How many faces, edges and vertices does a pyramid have with n sided polygon as its base?

Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?

In the given figures, identify the different shapes involved.

What figure is formed if only the height of a cube is increased or decreased?

Use isometric dot paper to draw figure.

A tetrahedron

Use isometric dot paper to draw figure.

A rectangular prism with length 4 units, width 2 units and height 2 units.

Identify the nets given below and mention the name of the corresponding solid in the space provided.

Nets |
Name of Solid |

(a) | |

(b) | |

(c) | |

(d) | |

(e) | |

(f) |

Draw a map of your school playground. Mark all necessary places like 2 library, Playground, Medical Room, Classrooms, Assembly area, etc.

Refer to the given map to answer the following questions.

What is the built-up area of Govt. Model School I?

Refer to the given map to answer the following questions.

Name the schools shown in the picture.

Refer to the given map to answer the following questions.

Which park is nearest to the dispensary?

Refer to the given map to answer the following questions.

To which block does the main market belong?

Refer to the given map to answer the following questions.

How many parks have been represented in the map?

Look at the map given below. Answer the following questions.

(a) Which two hospitals are opposite to each other?

(b) A person residing at Niti Bagh has to go to Chirag Delhi after dropping her daughter at Asiad Tower. Mention the important landmarks he will pass alongwith the roads taken.

(c) Name of which road is similar to the name of some month.

Look at the map given below

Houses

Now, answer the following questions.

Name the roads that meet at round about.

Look at the map given below

Houses

Now, answer the following questions.

Name the roads that meet at round about.

Look at the map given below

Houses

Now, answer the following questions.

On which road is the Police Station situated?

Look at the map given below

Houses

Now, answer the following questions.

If Ritika stays adjacent to bank and you have to send her a card, what address will you write?

Look at the map given below

Houses

Now, answer the following questions.

Which sector has maximum number of houses?

Look at the map given below

Houses

Now, answer the following questions.

In which sector is Fire Station located?

Look at the map given below

Houses

Now, answer the following questions.

In the map, how many sectors have been shown?

A photographer uses a computer program to enlarge a photograph. What is the scale according to which the width has enlarged?

The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?

The distance between school and house of a girl is given by 5 cm in a picture, using the scale 1 cm : 5 km. Find the actual distance between the two places?

Use a ruler to measure the distance in cm between the places joined by dotted lines. If the map has been drawn using the scale 1 cm : 10 km, find the actual distances between school and library

Use a ruler to measure the distance in cm between the places joined by dotted lines. If the map has been drawn using the scale 1 cm : 10 km, find the actual distances between college and complex

Use a ruler to measure the distance in cm between the places joined by dotted lines. If the map has been drawn using the scale 1 cm : 10 km, find the actual distances between house and school

The actual length of a painting was 2 m. What is its length in the photograph if the scale used is 1 mm : 20 cm.

Find the scale.

Actual size 12 m

Drawing size 3 cm

Find the scale.

Actual size 45 fee

Drawing size 5 inches

In a town, an ice cream parlour has displayed an ice cream sculpture of height 360 cm. The parlour claims that these ice creams and the sculpture are in the scale 1:30. What is the height of the ice creams served?

## Chapter 6: Visualising Solid Shapes

## NCERT solutions for Mathematics Exemplar Class 8 chapter 6 - Visualising Solid Shapes

NCERT solutions for Mathematics Exemplar Class 8 chapter 6 (Visualising Solid Shapes) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 8 chapter 6 Visualising Solid Shapes are Viewing Different Sections of a Solid, Mapping Space Around Us, Faces, Edges and Vertices, Plane Figures and Solid Shapes, Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism, Concept of Polyhedron, Concept of Prism, Concept of Pyramid, Euler's Formula.

Using NCERT Class 8 solutions Visualising Solid Shapes exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 6 Visualising Solid Shapes Class 8 extra questions for Mathematics Exemplar Class 8 and can use Shaalaa.com to keep it handy for your exam preparation