# NCERT solutions for Mathematics Exemplar Class 8 chapter 6 - Visualising Solid Shapes [Latest edition]

## Chapter 6: Visualising Solid Shapes

Exercise
Exercise [Pages 181 - 205]

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

#### Choose the correct alternative:

Exercise | Q 1 | Page 181

Which amongst the following is not a polyhedron?

Exercise | Q 2 | Page 181

Which of the following will not form a polyhedron?

• 3 triangle

• 2 triangles and 3 parallelogram

• 8 triangles

• 1 pentagon and 5 triangles

Exercise | Q 3 | Page 181

Which of the following is a regular polyhedron?

• Cuboid

• Triangular prism

• Cube

• Square prism

Exercise | Q 4 | Page 181

Which of the following is a two Dimensional figure?

• Rectangle

• Rectangular Prism

• Square Pyramid

• Square Prism

Exercise | Q 5 | Page 181

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

• Line segmen

• Circle

• Octagon

• Oval

Exercise | Q 6 | Page 181

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

• Pyramid

• Prism

• Cone

• Sphere

Exercise | Q 7 | Page 181

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

• Polyhedron

• Cone

• Cylinder

• Polygon

Exercise | Q 8 | Page 182

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

• 6

• 4

• 8

• 2

Exercise | Q 9 | Page 182

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

Exercise | Q 10 | Page 182

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

Exercise | Q 11 | Page 183

Which of the nets given below will generate a cone?

Exercise | Q 12 | Page 183

Which of the following is not a prism?

Exercise | Q 13 | Page 183

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

Exercise | Q 14 | Page 184

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

Exercise | Q 15 | Page 184

Which of the following shapes has a vertex?

Exercise | Q 16 | Page 184

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

Exercise | Q 17 | Page 185

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

Exercise | Q 18 | Page 185

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

Exercise | Q 19 | Page 185

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

Exercise | Q 20 | Page 186

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

• 1:2

• 2:1

• 2:3

• 3:2

Exercise | Q 21 | Page 186

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

• 4

• 3

• 5

• 2

#### Fill in the blanks:

Exercise | Q 22 | Page 186

Square prism is also called a ______.

Exercise | Q 23 | Page 186

Rectangular prism is also called a ______.

Exercise | Q 24 | Page 186

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

Exercise | Q 25 | Page 186

A pyramid on an n sided polygon has ______ faces.

Exercise | Q 26 | Page 186

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

Exercise | Q 27 | Page 186

The given net    can be folded to make a ______.

Exercise | Q 28 | Page 186

A solid figure with only 1 vertex is a ______.

Exercise | Q 29 | Page 186

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

Exercise | Q 30 | Page 186

The net of a rectangular prism has ______ rectangles.

Exercise | Q 31 | Page 187

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

Exercise | Q 32 | Page 187

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

Exercise | Q 33 | Page 187

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 ______.

Exercise | Q 34 | Page 187

A pentagonal prism has ______ faces.

Exercise | Q 35 | Page 187

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

Exercise | Q 36 | Page 187

is the ______ view of

Exercise | Q 37 | Page 187

The number of cubes in    are ______

Exercise | Q 38 | Page 187

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

Exercise | Q 39 | Page 187

Total number of regular polyhedra is ______.

Exercise | Q 40 | Page 188

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

Exercise | Q 41. (a) | Page 188

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

Exercise | Q 41. (b) | Page 188

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

Exercise | Q 41. (c) | Page 188

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

Exercise | Q 41. (d) | Page 188

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:

Exercise | Q 42 | Page 189

The other name of cuboid is tetrahedron.

• True

• False

Exercise | Q 43 | Page 189

A polyhedron can have 3 faces.

• True

• False

Exercise | Q 44 | Page 189

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

• True

• False

Exercise | Q 45 | Page 189

Regular octahedron has 8 congruent faces which are isosceles triangles.

• True

• False

Exercise | Q 46 | Page 190

Pentagonal prism has 5 pentagons.

• True

• False

Exercise | Q 47 | Page 190

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

• True

• False

Exercise | Q 48 | Page 190

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

• True

• False

Exercise | Q 49 | Page 190

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

• True

• False

Exercise | Q 50 | Page 190

The top view of

• True

• False

Exercise | Q 51 | Page 190

The number of edges in a parallelogram is 4.

• True

• False

Exercise | Q 52 | Page 190

Every solid shape has a unique net.

• True

• False

Exercise | Q 53 | Page 190

Pyramids do not have a diagonal.

• True

• False

Exercise | Q 54 | Page 190

The given shape is a cylinder.

• True

• False

Exercise | Q 55 | Page 190

A cuboid has atleast 4 diagonals.

• True

• False

Exercise | Q 56 | Page 190

All cubes are prisms

• True

• False

Exercise | Q 57 | Page 191

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

• True

• False

Exercise | Q 58 | Page 191

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

Exercise | Q 59 | Page 191

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

Exercise | Q 60 | Page 191

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

Exercise | Q 61 | Page 191

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

Exercise | Q 62 | Page 192

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
Exercise | Q 63.(a) | Page 192

How many faces does the following solids, have tetrahedron?

Exercise | Q 63.(b) | Page 192

How many faces does the following solids, have hexahedron?

Exercise | Q 63.(c) | Page 192

How many faces does the following solids have octagonal pyramid?

Exercise | Q 63.(d) | Page 192

How many faces does the following solids have octahedron?

Exercise | Q 64 | Page 193

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.

Exercise | Q 65.(a) | Page 193

How many vertices does the following solids have?

Cone

Exercise | Q 65.(b) | Page 193

How many vertices does the following solids have?

Cylinder

Exercise | Q 65.(c) | Page 193

How many vertices does the following solids have?

Sphere

Exercise | Q 65.(d) | Page 193

How many vertices does the following solids have?

Octagonal Pyramid

Exercise | Q 65.(e) | Page 193

How many vertices does the following solids have?

Tetrahedron

Exercise | Q 65.(f) | Page 193

How many vertices does the following solids have?

Hexagonal Prism

Exercise | Q 66.(a) | Page 193

How many edges does following solids have?

Cone

Exercise | Q 66.(b) | Page 193

How many edges does following solids have?

Cylinder

Exercise | Q 66.(c) | Page 193

How many edges does following solids have?

Sphere

Exercise | Q 66.(d) | Page 193

How many edges does following solids have?

Octagonal Pyramid

Exercise | Q 66.(e) | Page 193

How many edges does following solids have?

Hexagonal Prism

Exercise | Q 66.(f) | Page 193

How many edges does following solids have?

Kaleidoscope

Exercise | Q 67.(a) | Page 194

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

Exercise | Q 67.(b) | Page 194

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

Exercise | Q 67.(c) | Page 193

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

Exercise | Q 67.(d) | Page 193

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

Exercise | Q 67.(e) | Page 193

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

Exercise | Q 67.(f) | Page 193

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

Exercise | Q 67.(g) | Page 193

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

Exercise | Q 67.(h) | Page 193

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

Exercise | Q 67.(i) | Page 193

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

Exercise | Q 67.(j) | Page 193

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

Exercise | Q 67.(k) | Page 193

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

Exercise | Q 67.(l) | Page 193

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

Exercise | Q 67. (m) | Page 193

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

Exercise | Q 68.(a) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(b) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(c) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(d) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(e) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(f) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(g) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(h) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(i) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(j) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(k) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 68.(l) | Page 195

Count the number of cubes in the given shapes.

Exercise | Q 69.(a) | Page 196

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

Exercise | Q 69.(b) | Page 196

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

Exercise | Q 69.(c) | Page 196

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

Exercise | Q 69.(d) | Page 196

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

Exercise | Q 69.(e) | Page 196

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

Exercise | Q 69.(f) | Page 196

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

Exercise | Q 69.(g) | Page 196

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

Exercise | Q 69.(h) | Page 196

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

Exercise | Q 69.(i) | Page 196

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

Exercise | Q 69.(j) | Page 196

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

Exercise | Q 70.(i) | Page 197

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
Exercise | Q 70.(ii) | Page 197

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
Exercise | Q 70.(iii) | Page 197

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
Exercise | Q 70.(iv) | Page 197

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
Exercise | Q 70.(v) | Page 197

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
Exercise | Q 70.(vi) | Page 197

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
Exercise | Q 71 | Page 198

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

Exercise | Q 72 | Page 198

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

Exercise | Q 73 | Page 198

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

Exercise | Q 74. (a) | Page 198

Find the number of faces in the given shapes:

Exercise | Q 74. (b) | Page 198

Find the number of faces in the given shapes:

Exercise | Q 74. (c) | Page 198

Find the number of faces in the given shapes:

Exercise | Q 75 | Page 198

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

Exercise | Q 76 | Page 198

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

Exercise | Q 77 | Page 198

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

Exercise | Q 78 | Page 198

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

Exercise | Q 79 | Page 198

Draw the net of the following cuboid:

#### Match the following:

Exercise | Q 80 | Page 199
 Figure Name (a) (a) Hexahedron (b) (b) Hexagonal Prism (c) (c) Square Pyramid (d) (d) Cone
Exercise | Q 81 | Page 199

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
Exercise | Q 82 | Page 199

Draw the net of the following shape.

Exercise | Q 83 | Page 200

Draw the net of the following solid.

(Hint: Pentagons are not congruent.)

Exercise | Q 84 | Page 200

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

Exercise | Q 85 | Page 200

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

Exercise | Q 86 | Page 200

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

Exercise | Q 87 | Page 200

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

Exercise | Q 88 | Page 200

In the given figures, identify the different shapes involved.

Exercise | Q 89 | Page 200

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

Exercise | Q 90.(a) | Page 200

Use isometric dot paper to draw figure.

A tetrahedron

Exercise | Q 90.(b) | Page 200

Use isometric dot paper to draw figure.

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

Exercise | Q 91 | Page 201

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)
Exercise | Q 92 | Page 202

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

Exercise | Q 93.(a) | Page 202

Refer to the given map to answer the following questions.

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

Exercise | Q 93.(b) | Page 202

Refer to the given map to answer the following questions.

Name the schools shown in the picture.

Exercise | Q 93.(c) | Page 202

Refer to the given map to answer the following questions.

Which park is nearest to the dispensary?

Exercise | Q 93.(d) | Page 202

Refer to the given map to answer the following questions.

To which block does the main market belong?

Exercise | Q 93.(e) | Page 202

Refer to the given map to answer the following questions.

How many parks have been represented in the map?

Exercise | Q 94 | Page 203

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.

Exercise | Q 95. (a) | Page 203

Look at the map given below
Houses

Exercise | Q 95. (b) | Page 203

Look at the map given below
Houses

Exercise | Q 95. (c) | Page 203

Look at the map given below
Houses

On which road is the Police Station situated?

Exercise | Q 95. (d) | Page 203

Look at the map given below
Houses

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

Exercise | Q 95. (e) | Page 203

Look at the map given below
Houses

Which sector has maximum number of houses?

Exercise | Q 95. (f) | Page 203

Look at the map given below
Houses

In which sector is Fire Station located?

Exercise | Q 95. (g) | Page 203

Look at the map given below
Houses

In the map, how many sectors have been shown?

Exercise | Q 96 | Page 204

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

Exercise | Q 97 | Page 204

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?

Exercise | Q 98 | Page 204

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?

Exercise | Q 99.(a) | Page 205

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

Exercise | Q 99.(b) | Page 205

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

Exercise | Q 99.(c) | Page 205

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

Exercise | Q 100 | Page 205

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.

Exercise | Q 101.(a) | Page 205

Find the scale.
Actual size 12 m
Drawing size 3 cm

Exercise | Q 101.(b) | Page 205

Find the scale.
Actual size 45 fee
Drawing size 5 inches

Exercise | Q 102 | Page 205

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?

Exercise

## 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.

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