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NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes

NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes

Updated on Apr 20, 2025 06:56 PM IST

Have you ever wondered how architects design a building or how engineers create a 3D model of the building even before construction??? The concept of visualizing solid shapes plays a crucial role in these. Visualizing solid shapes is one of the essential skills in our day-to-day life, like arranging a set of items, packing certain items, assembling furniture, and so on. This interesting chapter helps students explore different types of 3D shapes like cubes, cuboids, cylinders, cones, etc. and their properties. It mainly focuses on the representation of these shapes in different views like top view, bottom view and side view. The NCERT Solutions of this chapter provide a clear explanation and step-by-step solutions for all the exercise questions.

This Story also Contains
  1. NCERT Solutions for Maths Chapter 13 Visualising Solid Shapes Class 7 - Notes
  2. NCERT Solutions for Maths Chapter 13 Visualising Solid Shapes Class 7
  3. NCERT Solutions for Class 7 Maths Chapter 13 Exercise
  4. Visualising Solid Shapes Class 7 Chapter 13-Topics
  5. NCERT Solutions for Class 7 Maths Chapter 13 Visualizing Solid Shapes - Points to Remember
  6. NCERT Solutions for Class 7 Maths Chapter Wise
  7. NCERT Solutions for Class 7 Subject Wise
  8. NCERT Books and NCERT Syllabus
NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes
NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes

These solutions will provide you with step-by-step explanations with conceptual clarity. These solutions are completely reliable as it is created by subject matter experts at Careers360. Students can also refer to NCERT Solutions for Class 7 Maths which give the step-by-step solution aligning the latest syllabus to all the chapters of Class 7 Maths.

NCERT Solutions for Maths Chapter 13 Visualising Solid Shapes Class 7 - Notes

Plane figures ⇒ 2D

Solid shapes ⇒ 3D

Cube: It is a 3D shape with 6 square faces, 12 edges and 8 vertices. It has equal length, breadth, and height as each face is a square. A dice is an example of a cube.

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Cuboid: It is a 3D shape with 6 rectangular faces, 12 edges, and 8 vertices. Its length, breadth, and height are unequal, and opposite faces are equal in area. A matchbox or a book is an example of a cuboid.

Cone: It is a 3D shape with one circular face (base), one curved surface, and one vertex (tip). It tapers smoothly from the base to the vertex. An ice cream cone is an example of a cone.

Sphere: It is a perfectly round 3D shape with no edges or vertices and one continuous curved surface. All points on its surface are equidistant from its centre. A ball is an example of a sphere.

Sphere

Cylinder: A cylinder is a 3D shape with 2 edges and no vertices. It has 3 faces - two circles and a rectangle wrapped around it. The top view of the cylinder is a circle. The vertical cross-section of the cylinder is rectangular in shape and the horizontal cross-section is circular in shape.

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NCERT Solutions for Maths Chapter 13 Visualising Solid Shapes Class 7

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NCERT Solutions for Class 7 Maths Chapter 13 Exercise

NCERT Solutions for Class 7 Maths Chapter 13

Visualizing Solid Shapes Exercise 13.1

Page Number: 202-203

Number of Questions: 5

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.

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

Answer:

The sum of the opposite sides of a dice =7

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

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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, in this case, one pair is 4 opposite to 1
So, their sum is equal to 5 and not equal to 7
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.)

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Answer:

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

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Question: 5 Match the nets with the appropriate solids:

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Answer:

These are the correct matches

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

NCERT Solutions for Class 7 Maths Chapter 13

Visualizing Solid Shapes Exercise 13.2

Page Number: 206-207

Number of Questions: 5

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 that are possible with the given dimensions of a cuboid.
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Question: 3 Three cubes, each with a 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 a 2 cm edge, are placed side by side to form a cuboid.

So, the oblique sketch of the cuboid is given below.

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

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Answer:

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

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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 some cubes or cuboids of the dimensions specified by your friend.

Answer:

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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
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NCERT Solutions for Class 7 Maths Chapter 13

Visualizing Solid Shapes Exercise 13.3

Page Number: 209

Number of Questions: 1

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

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A vertical cut gives a square or rectangular cross-section
ii) The horizontal cut gives a rectangular cross-section

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b) A round apple
In both cases, the cross-section will be circular in shape approximately

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c) A die
Both the cuts will give a square shape.

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d) A circular pipe

i) A vertical cut will give a circular shape

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ii) The horizontal cut gives a rectangular shape

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e) An ice cream cone

i) The vertical cut gives a triangular shape

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ii) The horizontal cut gives a circular shape

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NCERT Solutions for Class 7 Maths Chapter 13

Visualizing Solid Shapes Exercise 13.4

Page Number: 210-211

Number of Questions: 3

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 shadows only in the shape of a square.
Therefore, both statements (i) and (ii) are not possible

Visualising Solid Shapes Class 7 Chapter 13-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 13 Visualizing Solid Shapes - Points to Remember

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.

Different Shapes on Shadows: The shadow of a sphere will be circular in shape, the shadow of a cone will be triangular in shape, and 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.

NCERT Solutions for Class 7 Maths Chapter Wise


NCERT Solutions for Class 7 Subject Wise

Students can access the subject-wise solutions for Class 7 using the links below.

NCERT Books and NCERT Syllabus

Articles

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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