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

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes: 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.

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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.

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.

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

These are the correct matches

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

Question: Complete the following table:

 Faces (F) 6 4 Edges (E) 12 Vertices (V) 8 4

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

## NCERT Solutions for Class 7 Maths 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.

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

## NCERT Solutions for Class 7 Maths 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.

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

The sum of the opposite sides of a dice =7

Question: 3 Can this be a net for a die? Explain your 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: 4 Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here?
(Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)

There are three faces in the given net. The two possibilities of forming nets are

Question:5 Match the nets with appropriate solids:

Thsese are the correct matches

## NCERT Solutions 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.

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

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.

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

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

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

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.

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

## NCERT Solutions 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).

i) There are 4 columns and 2 rows in the first line.
So, the total number of cubes in the first line is

And there is total 3 such line.
Therefore, the total number of cubes are

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

And there are total 2 such lines
So, the total number of cubes at the bottom are
Now, we can see that two cubes are placed on the second line
Therefore, the total number of cubes are

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

And there are total 2 such lines
So, the total number of cubes at the bottom are
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

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)

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.

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

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 Class 7 Maths Chapter 15 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

a ) A brick

i ) Vertical cut

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

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

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

d ) A circular pipe

i ) A vertical cut will give a circular shape

ii ) The horizontal cut gives a rectangular shape

e ) An ice cream cone

i) The vertical cut gives a triangular shape

ii) The horizontal cut gives a circular shape

## NCERT Solutions for Class 7 Maths Chapter 15 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.

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 7 Maths 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.

For a )

For b)

For c)

For d)

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

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

i )
ii )

iii )

## 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 8 Comparing 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 15 Visualising Solid Shapes

### NCERT Solutions for Class 7 Subject Wise

 NCERT Solutions for Class 7 Maths NCERT Solutions for Class 7 Science

## 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!!!

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