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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.
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.
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.
Plane figures ⇒ 2D
Solid shapes ⇒ 3D
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.
Answer:
These are the correct matches
Question: Complete the following table:
Answer:
Faces (F) | 6 | 4 | 10 | 7 | |||
Edges (E) | 12 | 6 | 16 | 15 | |||
Vertices (V) | 8 | 4 | 9 | 10 |
Answer:
Out of these four nets, we can make a tetrahedron with net (i) and (iii)
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
Question: 3 Can this be a net for a die? Explain your answer.
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
Answer:
There are three faces in the given net. The two possibilities of forming nets are
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
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
Question: 4 Make an oblique sketch for each one of the given isometric shapes:
Answer:
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.
Answer:
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
Question: Try to guess the number of cubes in the following arrangements (Fig 15.17).
Answer:
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
(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
Answer:
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
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
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
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
Answer:
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.
Answer:
Drawn view of each solid as seen from the direction indicated by the arrow are : -
i )
ii )
iii )
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | Comparing quantities |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | Exponents and Powers |
Chapter 14 | |
Chapter 15 | Visualising Solid Shapes |
Happy learning!!!
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