NCERT Solutions for Class 8 Maths Chapter 6 - Visualising The Solid Shapes

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Question 1:

In the given question out of four options only one is correct. Write the correct answer.

Which amongst the following is not a polyhedron?

Question 2:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following will not form a polyhedron?
(a) 3 triangle
(b) 2 triangles and 3 parallelogram
(c) 8 triangles
(d) 1 pentagon and 5 triangles

Question 3:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following is a regular polyhedron?
(a) Cuboid
(b) Triangular prism
(c) Cube
(d) Square prism

Question 4:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following is a two Dimensional figure?
(a) Rectangle
(b) Rectangular Prism
(c) Square Pyramid
(d) Square Prism

Question 5:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following can be the base of a pyramid?
(a) Line segment
(b) Circle
(c) Octagon
(d) Oval

Question 6:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following 3D shapes does not have a vertex?
(a) Pyramid
(b) Prism
(c) Cone
(d) Sphere

Question 7:

In the given question out of four options only one is correct. Write the correct answer.
Solid having only line segments as its edges is a
(a) Polyhedron
(b) Cone
(c) Cylinder
(d) Polygon

Question 8:

In the given question out of four options only one is correct. Write the correct answer.
In a solid if F = V = 5, then the number of edges in this shape is
(a) 6
(b) 4
(c) 8
(d) 2

Question 9:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following is the top view of the given shape?

Question 10:

In the given question out of four options only one is correct. Write the correct answer.
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?

Question 11:

In the given question out of four options only one is correct. Write the correct answer.
Which of the nets given below will generate a cone?

Question 12:

In the given question out of four options only one is correct. Write the correct answer.

Which of the following is not a prism?

Question 13:

In the given question out of four options only one is correct. Write the correct answer.
We have 4 congruent equilateral triangles. What do we need more to make a pyramid?
(a) An equilateral triangle.
(b) A square with same side length as of triangle.
(c) 2 equilateral triangles with side length same as triangle.
(d) 2 squares with side length same as triangle.
 

Question 14:

In the given question out of four options only one is correct. Write the correct answer.
Side of a square garden is 30 m. If the scale used to draw its picture is 1 cm: 5m, the perimeter of the square in the picture is
(a) 20 cm
(b) 24 cm
(c) 28 cm
(d) 30 cm

Question 15:

In the given question out of four options only one is correct. Write the correct answer.

Which of the following shapes has a vertex.

Question 16:

In the given question out of four options only one is correct. Write the correct answer.

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

Question 17:

In the given question out of four options only one is correct. Write the correct answer.
Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(b) V = 6, F = 8, E = 12
(c) V = 20, F = 12, E = 30
(d) V = 4, F = 6, E = 6

Question 18:

In the given question out of four options only one is correct. Write the correct answer.
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
(a) 1:11
(b) 1:10
(c) 1:100
(d) 1:3

Question 19:

In the given question out of four options only one is correct. Write the correct answer.
The following is the map of a town. Based on it answer question 19-21.

Question 20:

In the given question out of four options only one is correct. Write the correct answer.
The following is the map of a town. Based on it answer question 19-21.

The ratio of the number of general stores and that of the ground is
(a) 1 : 2
(b) 2 : 1
(c) 2 : 3
(d) 3 : 2

Question 21:

In the given question out of four options only one is correct. Write the correct answer.
The following is the map of a town. Based on it answer question 19-21.

According to the map, the number of schools in the town is
(a) 4
(b) 3
(c) 5
(d) 2

Question 22:

Fill in the blanks to make the statements true.
Square prism is also called a _______.

Question 23:

Fill in the blanks to make the statements true.
Rectangular prism is also called a ________.

Question 24:

Fill in the blanks to make the statements true.
In the figure, the number of faces meeting at B is ________.

Question 25:

Fill in the blanks to make the statements true.
A pyramid on an n sided polygon has ______ faces.

Question 26:

Fill in the blanks to make the statements true.
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.

Question 27:

Fill in the blanks to make the statements true.
The given net can be folded to make a ______.

Question 28:

Fill in the blanks to make the statements true.
A solid figure with only 1 vertex is a ______.

Question 29:

Fill in the blanks to make the statements true.
Total number of faces in a pyramid which has eight edges is______.

Question 30:

Fill in the blanks to make the statements true.
The net of a rectangular prism has ______ rectangles.

Question 31:

Fill in the blanks to make the statements true.
In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the ______ face.

Question 32:

Fill in the blanks to make the statements true.
If 4 km on a map is represented by 1 cm, then 16 km is represented by ______ cm.

Question 33:

Fill in the blanks to make the statements true.
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 ______.

Question 34:

Fill in the blanks to make the statements true.
A pentagonal prism has ______ faces.

Question 35:

Fill in the blanks to make the statements true.
If a pyramid has a hexagonal base, then the number of vertices is ______.

Question 36:

Fill in the blanks to make the statements true.
is the _______ view of

Question 37:

Fill in the blanks to make the statements true.
The number of cubes in  are ______.

Question 38:

Fill in the blanks to make the statements true.
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.

Question 39:

Fill in the blanks to make the statements true.
Total number of regular polyhedron is ______.

Question 40:

Fill in the blanks to make the statements true.
A regular polyhedron is a solid made up of ______ faces.

Question 41:

Fill in the blanks to make the statements true.
For each of the following solids, identify the front, side and top views and write it in the space provided.








 

Question 42:

State whether the following statements are true (T) or false (F).
The other name of cuboid is tetrahedron.

Question 43:

State whether the following statements are true (T) or false (F).
A polyhedron can have 3 faces.

Question 44:

State whether the following statements are true (T) or false (F).
A polyhedron with least number of faces is known as a triangular pyramid.

Question 45:

State whether the following statements are true (T) or false (F).
Regular octahedron has 8 congruent faces which are isosceles triangles.

Question 46:

State whether the following statements are true (T) or false (F).
Pentagonal prism has 5 pentagons.

Question 47:

State whether the following statements are true (T) or false (F).
Every cylinder has 2 opposite faces as congruent circles, so it is also a prism.

Question 48:

State whether the following statements are true (T) or false (F).
Euler’s formula is true for all three-dimensional shapes.

Question 49:

State whether the following statements are true (T) or false (F).
A polyhedron can have 10 faces, 20 edges and 15 vertices.

Question 50:

State whether the following statements are true (T) or false (F).
The top view of  is

Question 51:

State whether the following statements are true (T) or false (F).
The number of edges in a parallelogram is 4.

Question 52:

State whether the following statements are true (T) or false (F).
Every solid shape has a unique net.

Question 53:

State whether the following statements are true (T) or false (F).
Pyramids do not have a diagonal.

Question 54:

State whether the following statements are true (T) or false (F).
The given shape is a cylinder. 

Question 55:

State whether the following statements are true (T) or false (F).
A cuboid has at least 4 diagonals.

Question 56:

State whether the following statements are true (T) or false (F).
All cubes are prisms.

Question 57:

State whether the following statements are true (T) or false (F).
A cylinder is a 3-D shape having two circular faces of different radii.

Question 58:

State whether the following statements are true (T) or false (F).

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.

Question 59:

State whether the following statements are true (T) or false (F).
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.

Question 60:

State whether the following statements are true (T) or false (F).
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.

Question 61:

State whether the following statements are true (T) or false (F).
The actual width of a store room 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.

Question 62:

Complete the table given below:

S. No	Solid	Shape of Solid	Number of faces F	Number of Vertices 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

Question 63:

How many faces does each of the following solids, have?
(a) Tetrahedron
(b) Hexahedron
(c) Octagonal Pyramid
(d) Octahedron

Question 64:

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.

Question 65:

How many vertices does each of the following solids have?
(a) Cone
(b) Cylinder
(c) Sphere
(d) Octagonal Pyramid
(e) Tetrahedron
(f) Hexagonal Prism

Question 66:

How many edges does each of following solids have?
(a) Cone
(b) Cylinder
(c) Sphere
(d) Octagonal Pyramid
(e) Hexagonal Prism
(f) Kaleidoscope

Question 67:

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

Question 68:

Count the number of cubes in the given shapes.

Question 69:

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

 

(a)	(b)	(c)	(d)	(e)	(f)

(g)	(h)	(i)	(j)

Question 70:

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

Question 71:

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

Question 72:

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

Question 73:

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

Question 74:

Find the number of faces in the given shapes:

Question 75:

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

Question 76:

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

Question 77:

Draw the net of a regular hexahedron with side 3 cm.

Question 78:

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

Question 79:

Draw the net of the following cuboid:

Question 80:

Match the following:
 

	Figure		Name
(a)		(a)	Hexahedron
(b)		(b)	Hexagonal Prism
(c)		(c)	Square Pyramid
(d)		(d)	Cone

Question 81:

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

Question 82:

Draw the net of the following shape.

Question 83:

Draw the net of the following solid.
 

Question 84:

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

Question 85:

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

Question 86:

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

Question 87:

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

Question 88:

In the given figures, identify the different shapes involved.

Question 89:

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

Question 90:

Use isometric dot paper to draw each figure.
(a) A tetrahedron.
(b) A rectangular prism with length 4 units, width 2 units and height 2 units.

Question 91:

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)

Question 92:

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

Question 93:

Refer to the given map to answer the following questions.
 

(a) What is the built-up area of Govt. Model School I ?
(b) Name the schools shown in the picture.
(c) Which park is nearest to the dispensary?
(d) To which block does the main market belong?
(e) How many parks have been represented in the map?

Question 94:

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 along with the roads taken.
(c) Name of which road is similar to the name of some month.

Question 95:

Look at the map given below.
$\boxed{ } \mathrm{Houses}$

Now answer the following questions.
(a) Name the roads that meet at round about.
(b) What is the address of the stadium?
(c) On which road is the Police Station situated?
(d) If Ritika stays adjacent to bank and you have to send her a card, what address will you write?
(e) Which sector has maximum number of houses?
(f) In which sector is Fire Station located?
(g) In the map, how many sectors have been shown?

Question 96:

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

Question 97:

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?

Question 98:

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?

Question 99:

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
(1) School and Library
(2) College and Complex
(3) House and School

Question 100:

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.

Question 101:

Find the scale.

(a) Actual size 12 m

Question 102:

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?