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NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes - Download PDF

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes - Download PDF

Edited By Ravindra Pindel | Updated on Feb 07, 2024 06:25 PM IST

NCERT Solutions for Maths Chapter 15 Visualising Solid Shapes Class 7: You have already learnt about the 2D geometry like a circle, square, a rectangle or a rhombus which are measured by length and width. We live in a world where every object that we can see or touch has three dimensions length, width, and height. For example, a cricket ball, an ice cream cone, a book, room, etc are solid figures which has three dimensions. These objects can be described by 3-dimensions length, width, and height. In CBSE NCERT solutions for Class 7 Maths chapter 15 Visualising solid shapes, you will get questions related to identifying the solid shapes and drawing isometric sketches for solid shapes. When you see 3-dimensional objects from different positions or different angles it looks different. In solutions of NCERT for Class 7 Maths chapter 15 Visualising Solid Shapes, you will get many questions related to isometric view of solid shape from different sides and angles which will give you more clarity of the concept. Let's understand this NCERT chapter with some basic solid shapes.

Cube:- Below given shape is known as a cube. It has equal length, breadth, and height. It consists of 6 faces, 12 edges and 8 vertices. Dice is an example of a cube.

1658744909606

Cylinder:- Below given shape is known as a cylinder. The horizontal crosssection of the cylinder is rectangular in shape and the vertical cross-section is circular in shape.

1658745578371

The shadow of a sphere will be circular in shape, the shadow of a cone will be triangular in shape, the shadow of the cylinder will be rectangular in shape. In simple words, this shadow is known as a plane view of a solid shape. There are 14 questions in 4 exercises of this chapter. You will get detailed explanations of all these questions in the NCERT Solutions for Class 7 . You can get NCERT Solutions from Classes 6 to 12 for Science and Maths by clicking on the above link.

Doing all the questions and activities of Solutions for NCERT Class 7 Maths Chapter 15 Visualising Solid Shapes will be interesting.

NCERT Solutions for Maths Chapter 15 Visualising Solid Shapes Class 7 - Important Formulae

Plane figures ⇒ 2D

Solid shapes ⇒ 3D

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes - Important Points

Vertices: Corner of solid shapes.

Edges: Line segment of solid skeleton.

Faces: Flat surface of a solid.

Oblique Sketch: It does not have proportional lengths of solid.

Isometric Sketch: It has proportional measurements of a solid.

Free download NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes PDF for CBSE Exam.

NCERT Solutions for Maths Chapter 15 Visualising Solid Shapes Class 7th

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NCERT Solutions for Class 7 Maths Chapter 15 Questions and Exercise

NCERT Solutions for Maths Chapter 15 Visualising Solid Shapes Class 7 Topic 15.1
Question: 1
Match the shape with the name:

45445616162

Answer:

These are the correct matches

(i)\rightarrow (b)
(ii)\rightarrow (d)
(iii)\rightarrow (a)
(iv)\rightarrow (c)
(v)\rightarrow (f)
(vi)\rightarrow (e)

NCERT Solutions for Maths Chapter 15 Visualising Solid Shapes Class 7 Topic 15.2

Question: Complete the following table:


15444541 151544411546 1454 11
Faces (F) 6 4

Edges (E) 12


Vertices (V) 8 4








Answer:


15444541
151544411546
1454
11
Faces (F) 6 4 10 7
Edges (E) 12 6 16 15
Vertices (V) 8 4 9 10


NCERT Solutions for Class 7th Math Chapter 15 Visualising Solid Shapes Topic 15.3

Question: 1 Here you find four nets (Fig 15.10). There are two correct nets among them to make a tetrahedron. See if you can work out which nets will make a tetrahedron.

154454

Answer:

Out of these four nets, we can make a tetrahedron with net (i) and (iii)

NCERT Solutions for Class 7th Math Chapter 15 Visualising Solid Shapes Exercise 15.1

Question:2 Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them. Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box.

144432326

145454

Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.

Answer:

The sum of the opposite sides of a dice =7

1643022788344

Question: 3 Can this be a net for a die? Explain your answer.

15454

Answer:

NO,
This can not be a net for a die because the opposite faces of a die always have a total sum of 7.
Now, this case one pair is 4 opposite to 1
So, their sum is equal to 5 and not equal to 7
And also, the 2nd pair is 6 opposite to 3 .
So, their sum is equal to 9 and not equal to 7

Question:5 Match the nets with appropriate solids:

14788

Answer:

Thsese are the correct matches

(a) \rightarrow (ii)
(b) \rightarrow (iii)
(c) \rightarrow (iv)
(d) \rightarrow (i)

NCERT Solution for Class 7 Maths Chapter 15 Visualising Solid Shapes Exercise 15.2

Question: 2 The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.

Answer:

There are a total of 3 isometric sketches of the cuboid are possible with given dimensions of a cuboid
1643022869947

1643022885564

1643022900104 1643022920323

Question: 3 Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.

Answer:

It is given that three cubes each with 2 cm edge are placed side by side to form a cuboid

So, the oblique sketch of the cuboid is given below

1643022952992
1643022966978

Question: 4 Make an oblique sketch for each one of the given isometric shapes:

1456232

Answer:

Oblique sketch for each one of the given isometric shapes is: -

16430230088061643023025737
1643023128622

1643023153173

Question: 5 Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)
(b) A cube with an edge 4 cm long.
An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.

Answer:

1643023201204

The isometric sketch of s cuboid of dimensions 5 cm, 3 cm and 2 cm. In a similar way, we can draw for the cube also
1643023216519

NCERT Solution for Class 7 Maths Chapter 15 Visualising Solid Shapes Topic 15.4.3

Question: Try to guess the number of cubes in the following arrangements (Fig 15.17).

1465462323

Answer:

i) There are 4 columns and 2 rows in the first line.
So, the total number of cubes in the first line is
\Rightarrow 4 \times 2 = 8
And there is total 3 such line.
Therefore, the total number of cubes are \Rightarrow 8\times 3 = 24

ii) There are 3 columns and 1 row in the first line at the bottom.
So, the total number of cubes in the first line are
\Rightarrow 3 \times 1 = 3
And there are total 2 such lines
So, the total number of cubes at the bottom are \Rightarrow 3 \times 2 = 6
Now, we can see that two cubes are placed on the second line
Therefore, the total number of cubes are \Rightarrow 6+2=8

iii) There are 3 columns and 1 row in the first line at the bottom.
So, the total number of cubes in the first line are
\Rightarrow 3 \times 1 = 3
And there are total 2 such lines
So, the total number of cubes at the bottom are \Rightarrow 3 \times 2 = 6
Now, we can see that two cubes are placed on the second line and one cube in the front of the first line
Therefore, the total number of cubes are \Rightarrow 6+3=9

Question:1 Two dice are placed side by side as shown: Can you say what the total would be on the face opposite to
(a) 5 + 6 (b) 4 + 3

(Remember that in a die sum of numbers on opposite faces is 7)

Answer:

a ) Face opposite to 5 is 2 and opposite to 6 is 1
Therefore, there sum is equal to = 2 + 1 = 3

b ) Face opposite to 4 is 3 and opposite to 3 is 4
Therefore, there sum is equal to = 3 + 4 = 7

Question:2 Three cubes each with 2 cm edge are placed side by side to form a cuboid. Try to make an oblique sketch and say what could be its length, breadth and height.

Answer:

Oblique sketch of three cubes each with 2 cm edge placed side by side to each other to form a cuboid is

1643023253842 In this case
lenght = 2+2+2= 6cm
breath = 2 cm
height = 2cm

Two more cases are possible with

Height = 2+2+2= 6cm
breath = 2 cm
length = 2cm

And

breath = 2+2+2= 6cm
length = 2 cm
height = 2cm

NCERT Solutions for Chapter 15 Maths Class 7 Visualising Solid Shapes Exercise 15.3

Question: 1 What cross-sections do you get when you give a

(i) vertical cut (ii) horizontal cut

to the following solids?

(a) A brick (b) A round apple (c) A die (d) A circular pipe (e) An ice cream cone

Answer:

a ) A brick

i ) Vertical cut

1643023298418 A vertical cut gives a square or rectangular crossection
ii ) The horizontal cut gives rectangular crossection

1643023313690 b ) A round apple
In both, the case crossection will be circular in shape approximately

1643023325055 c ) A die
both the cut will give a square shape

1643023337812 d ) A circular pipe

i ) A vertical cut will give a circular shape

1643023360533 ii ) The horizontal cut gives a rectangular shape

1643023373874 e ) An ice cream cone

i) The vertical cut gives a triangular shape

1643023387827 ii) The horizontal cut gives a circular shape

1643023399906

NCERT Solutions for Chapter 15 Maths Class 7 Visualising Solid Shapes Exercise 15.4

Question: 3 Examine if the following are true statements:

(i) The cube can cast a shadow in the shape of a rectangle.
(ii) The cube can cast a shadow in the shape of a hexagon.

Answer:

A cube can cast shadow only in the shape of a square.
Therefore, both statements (i) and (ii) are not possible

NCERT Solutions for Class 7th Math Chapter 15 Visualising Solid Shapes Topic 15.5.3

Question:1 For each solid, the three views (1), (2), (3) are given. Identify for each solid the corresponding top, front and side views.

1643023436701

Answer:

For a )

(1) \rightarrow Front/top
(2) \rightarrow Side
(3) \rightarrow Front/top

For b)

(1) \rightarrow Top
(2) \rightarrow Side
(3) \rightarrow Front

For c)

(1) \rightarrow Side
(2) \rightarrow Front
(3) \rightarrow Top

For d)

(1) \rightarrow Side
(2) \rightarrow Top
(3) \rightarrow Front

Question:2 Draw a view of each solid as seen from the direction indicated by the arrow.

115487

Answer:

Drawn view of each solid as seen from the direction indicated by the arrow are : -

i )
1643023487833 ii )
1643023500127
iii )
1643023510794

visualising solid shapes Class 7 Chapter 15-Topics

  • Introduction: Plane Figures And Solid Shapes
  • Faces, Edges And Vertices
  • Nets For Building 3-d Shapes
  • Drawing Solids On A Flat Surface
  • Oblique Sketches
  • Isometric Sketches
  • Viewing Different Sections Of A Solid
  • One Way To View An Object Is By Cutting Or Slicing
  • Another Way Is By Shadow Play
  • A Third Way Is By Looking At It From Certain Angles To Get Different Views

NCERT Solutions for Class 7 Maths Chapter Wise

Chapter No.

Chapter Name

Chapter 1

Integers

Chapter 2

Fractions and Decimals

Chapter 3

Data Handling

Chapter 4

Simple Equations

Chapter 5

Lines and Angles

Chapter 6

The Triangle and its Properties

Chapter 7

Congruence of Triangles

Chapter 8Comparing quantities

Chapter 9

Rational Numbers

Chapter 10

Practical Geometry

Chapter 11

Perimeter and Area

Chapter 12

Algebraic Expressions

Chapter 13

Exponents and Powers

Chapter 14

Symmetry

Chapter 15Visualising Solid Shapes

NCERT Solutions for Class 7 Subject Wise

Benefits of NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

  • There are some questions to make an isometric shape using paper which you should try at your home to visualize and understand it better.
  • These NCERT solutions will make your homework easy as you will find the detailed explanations of all the NCERT questions including practice questions given below every topic.
  • As the name suggests this chapter is more about visualizing and drawing the front view, side view, and top view and the isometric view of the solid shapes. In CBSE NCERT solutions for Class 7 Maths chapter 15 Visualising Solid Shapes, you will get step-by-step explanations to draw all the projection view from the solid shape and the isometric view from the projected view.

Happy learning!!!

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. What is plane figures?

The Figure which has only the length and breadth is called a plane figures. To get deeper understanding of these concepts study visualising solid shapes class 7 pdf which can be downloaded using link given above in this article. Also can practice chapter 15 hindi class 7 pdf if you are comfortable reading Hindi. 

2. What is covered in Class 7 Hindi Chapter 15

Class 7th hindi chapter 15 likely covers concepts related to visualizing and understanding solid shapes such as Faces, Edges And Vertices.

NCERT solutions for class 7 hindi chapter 15 focus on introducing various three-dimensional shapes and their properties, such as cubes, cuboids, cylinders, spheres, cones, and pyramids.

Students learn about different facets, vertices, and edges of these shapes, as well as their real-world examples. Students can practice class 7 hindi chapter 15 question answer pdf to get deeper understandig of the concepts.

3. What are the topics covered in NCERT Class 7 chapter 15?

 

Here are the topics covered in NCERT Class 7 chapter 15 

  • Introduction: Plane Figures And Solid Shapes  
  • Faces, Edges And Vertices  
  • Nets For Building 3-d Shapes  
  • Drawing Solids On A Flat Surface  
  • Oblique Sketches  
  • Isometric Sketches  
  • Viewing Different Sections Of A Solid  
  • One Way To View An Object Is By Cutting Or Slicing  
  • Another Way Is By Shadow Play  
  • A Third Way Is By Looking At It From Certain Angles To Get Different Views

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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