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By Maitree Choube
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Updated on 11 Nov 2025, 16:17 IST
Students may download NCERT Solutions for Class 7 Maths Chapter 13 PDF from INFINITY learn's official website. The fundamentals of drawing 3-D figures are explained in Chapter 13 of Visualising Solid Shapes for Class 7 according to the NCERT syllabus. It also explains how to recognize and count vertices, edges, and faces. This is the fundamental principle of solid shape visualization and how we might apply it in our daily lives.
To prepare for their upcoming exams, students can also obtain NCERT Solution PDF for all courses.
In Chapter 13 Visualising Solid Shapes of the NCERT Solutions for Class 7 Maths, there are four exercises. The solutions are provided to all the questions found in the exercises.
This chapter teaches about visualizing, drawing and identification of solid shapes under various positions like top, front and side. It too discusses such areas as nets of solid shapes, faces, edges, vertices, differences 2D and 3D and mapping locations. These concepts could be easily learned with the help of diagrams, solved problems, and practice questions, which are presented in NCERT Solutions of Class 7 Maths Chapter 13 and provide the student with the chance to develop imagination and geometry skills.
Solid shapes may be present in the form of laptops, mobile phones, computers, ice cream cones, tin cans and so on. These solid shapes have length, breadth and height.
Facts:
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Also Check: NCERT Solutions Class 7 Maths Chapter 9 Perimeter and Area
The NCERT solutions Class 7 maths Chapter 13 has some activities that will allow the students to comprehend the three-dimensional space and how some objects may be built in 3D.
The solutions given in the PDF are prepared by subject experts and follow the latest CBSE syllabus 2025–26, which makes learning accurate and updated. Each answer is explained step by step, so anyone can easily grasp the logic behind every problem.
By practicing from this Visualising Solid Shapes PDF, one will be able to improve basics, gain confidence, and handle Maths questions in exams with ease. The simple explanations, diagrams, and exercises help to visualize 3D shapes better. Class 7 maths visualising solid shapes pdf will help in revision and build strong problem-solving skills.
Download the NCERT Class 7 Maths Chapter 13 Question answer PDF now and make Maths easy and scoring subject
Geometry is a division of mathematics that is concerned with space. It is also useful in determining distances and heights in our world, whether it is the size of a box or the size of a room. Therefore, it is crucial that the students should pass through the theories of imagining solid shapes. The NCERT Solutions for class 7 Maths Chapter 1 include 4 exercises whose detailed answer explanation is given in this blog. students can solve this NCERT Solutions for Class 7 Maths Chapter 13 and check their answers.
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| S.No. | Exercise | Number of Questions |
| 1 | Class 7 Maths Chapter 13 – Exercise 15.1 | 5 Questions |
| 2 | Class 7 Maths Chapter 13 – Exercise 15.2 | 5 Questions |
| 3 | Class 7 Maths Chapter 13 – Exercise 15.3 | 1 Question |
| 4 | Class 7 Maths Chapter 13 – Exercise 15.4 | 3 Questions |
Also Check: NCERT Solutions Class 7 Maths Data Handling
Q1. Identify the nets which can be used to make cubes.
Answer: The correct nets are (ii), (iii), (iv), and (vi).
These nets can fold perfectly to form a cube because each has six equal squares joined in a way that every face connects properly.
Q2. Dice are cubes with dots on each face. Opposite faces always add up to 7.
Fill in the missing numbers on the nets below.
Answer:
Opposite faces are:
1 ↔ 6, 2 ↔ 5, 3 ↔ 4
This rule keeps the dice pattern correct, as on every real die the total on opposite faces equals 7.
Q3. Can this be a net for a die? Explain.
Given:
Fig: Refer PDF
Answer: No, this cannot be a correct net for a die because the opposite faces here do not total to 7.
For example, 1 is opposite 4 (sum = 5) and 3 is opposite 6 (sum = 9), both incorrect.
Q4. Here is an incomplete net for making a cube. Complete it in two different ways.
Answer:
A cube has 6 faces, so the net must have 6 squares connected edge to edge.
There are two possible ways to complete it by attaching the missing squares in different positions (students can draw these arrangements on squared paper).
Q5. Match the nets with their corresponding solids.
| S.No. | Net — Solid |
| 1 | (a) — (ii) |
| 2 | (b) — (iii) |
| 3 | (c) — (iv) |
| 4 | (d) — (i) |
Answer: Each net matches with the solid shape that it can form when folded.
Q1. Use isometric dot paper and make isometric sketches of the given solids.
Answer: Students can try this using isometric dot paper. Each vertex should be joined using slanting lines to show 3D effect.
Q2. Draw three different isometric sketches of a cuboid of dimensions 5 cm × 3 cm × 2 cm.
Answer: Try to draw the cuboid with different orientations — horizontal, vertical, and tilted — on isometric dot paper.
Q3. Three cubes of edge 2 cm are placed side by side to form a cuboid. Draw its isometric or oblique sketch.
Answer: Combine three 2 cm cubes in a row; the final shape looks like a cuboid of 6 cm × 2 cm × 2 cm.
Q4. Make an oblique sketch for each of the given isometric shapes.
Answer: Students can practice this by first drawing the front face and then adding the depth using slanting lines.
Q5. Draw (i) an oblique sketch and (ii) an isometric sketch for:
(a) A cuboid 5 cm × 3 cm × 2 cm
(b) A cube with edge 4 cm.
Answer:
(a) The cuboid sketch will show different lengths, widths, and heights.
(b) The cube sketch will have equal sides and all edges of equal length.
(Each can be drawn in more than one way as the shape can be viewed differently.)
Q1. What cross-sections do you get on cutting these solids:
(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:
| S.No. | Solid | Vertical Cut (Cross-section) | Horizontal Cut (Cross-section) |
| 1 | A brick | Rectangle (or square, depending on how you cut) | Rectangle |
| 2 | A round apple | Circle | Circle |
| 3 | A die (cube) | Square | Square |
| 4 | A circular pipe | Rectangle (if cut along its length) | Circle (when cut across) |
| 5 | An ice-cream cone | Triangle | Circle |
Each shape gives a different 2D figure when sliced in vertical or horizontal direction.
Q1. A bulb is kept above the following solids. Name the shape of the shadow in each case:
(i) A ball → Circle (shadow of a sphere)
(ii) A cylindrical pipe → Rectangle or Circle depending on direction
(iii) A book → Rectangle
Q2. Match the shadows with their solids:
| S.No. | Shadow — Possible Solids |
| 1 | Square — Cube |
| 2 | Circle — Sphere or Cylinder |
| 3 | Triangle — Cone or Pyramid |
| 4 | Rectangle — Cuboid or Cylinder |
Answer: The shape of the shadow changes with the angle of light.
Q3. Examine these statements:
(i) A cube can cast a shadow in the shape of a rectangle.
True – when light falls diagonally.
(ii) A cube can cast a shadow in the shape of a hexagon.
False – a cube has square faces only; a hexagonal shadow is not possible.
This chapter helps students:
| S.No. | Topic | Description / Key Points | Examples |
| 1 | 2-Dimensional Shapes | 2-D shapes have only length and breadth. They can be drawn on a flat surface and depend on two coordinates. | Square, Rectangle, Triangle, Circle, etc. |
| 2 | 3-Dimensional Shapes | 3-D shapes have length, breadth, and height. They have depth and occupy space. They can be touched and seen from different sides. | Cone, Cylinder, Sphere, Prism, Cube, Cuboid, etc. |
| 3 | Faces, Edges, and Vertices | Face – Flat surface of a solid. Edge – Line joining two corners. Vertices – Meeting points or corners of a solid. | Cube → 6 faces, 12 edges, 8 vertices. Formula: F – E + V = 2 |
| 4 | Basic 2-D Shapes | Square: Four equal sides, four corners. Rectangle: Four sides, opposite sides equal. Triangle: Three sides, three corners. | Square → Chessboard, Napkin Rectangle → Table, Laptop Triangle → Traffic light frame |
| 5 | Common 3-D Solids | Cuboid: Six flat faces, 12 edges, 8 vertices. Cube: All sides equal, 6 faces, 8 vertices. Cylinder: 1 curved face + 2 flat faces. Cone: 1 curved face + 1 flat circular base. | Cuboid → Book, Lunch Box Cube → Dice, Sugar Cube Cylinder → Tin Can, Candle Cone → Ice Cream Cone, Funnel |
| 6 | Solid Shape Sketches | Oblique Sketch: Drawn on squared paper; approximate view. Isometric Sketch: Drawn on 3D grid; shows actual proportion. We can view solids from the front, top, or side and see 2D shadows or cross-sections. | Used for drawing boxes, prisms, and everyday 3D objects. |
| 7 | More Solid Shapes | Triangular Prism: 5 faces, 9 edges, 6 vertices. Triangular Pyramid (Tetrahedron): 4 faces, 6 edges, 4 vertices. Square Pyramid: 5 faces, 8 edges, 5 vertices. Sphere: 1 curved surface, no edges or vertices. | Prism → Kaleidoscope Pyramid → Temple tops Sphere → Football, Globe |
| 8 | Polyhedrons | A solid made of polygonal faces. Spheres, cones, and cylinders are not polyhedrons. There are two types: Convex and Regular Polyhedrons. | Cube, Cuboid, Prism, Pyramid |
| 9 | Convex Polyhedrons | Any line joining two points on the surface lies completely inside or on the solid. | All regular solids like cube and prism |
| 10 | Regular Polyhedrons | All faces are regular polygons and meet evenly at each vertex. | Cube, Regular Tetrahedron |
| 11 | Prisms | A prism is a solid with identical top and base connected by parallelogram sides. The bases can be of any polygon. | Triangular Prism, Rectangular Prism, Pentagonal Prism |
| 12 | Pyramids | A pyramid has a polygonal base and triangular sides that meet at a common vertex. | Triangular Pyramid, Square Pyramid, Hexagonal Pyramid |
| 13 | Nets for Building 3-D Shapes | A net is a 2D pattern that can be folded to make a 3D solid. It helps in understanding surface area and structure. | Cube Net, Cuboid Net, Pyramid Net |
Using Infinity Learn NCERT Solutions for Class 7 Maths, will realize how much easier it became to understand every concept clearly.
These solutions are based on latest CBSE syllabus 2025–26 and explain each topic in a simple, step-by-step manner. Examples used in this pdf are practical and relatable, and every exercise follows the same format as NCERT textbook, which helps to prepare well for exams.
By studying from Infinity Learn’s Class 7 Maths NCERT Solutions, one can revise faster, clear your doubts instantly, and gain confidence before tests.
Students can also get complete study resource for Class 7 that will help them in scoring full marks in their exam.
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NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes very helpful because they explain every concept clearly with diagrams and examples. These solutions make it easy to understand 3D figures, nets, and views which are also useful for higher classes and CBSE board exams
Yes, try to practice all the exercises because each exercise teaches a new concept like identifying nets, drawing 3D sketches, or finding cross-sections. The more you practice, the better you will understand how 2D shapes form 3D solids, which makes Maths much easier during exams.
This chapter covers several important topics like:
Sometimes, students draw incorrect nets where faces don’t connect properly or the folding doesn’t form a complete solid. The NCERT Solutions help by giving step-by-step diagrams and examples of correct nets. This way, one can easily see which nets actually make cubes or cuboids and which ones don’t.
The key formulas to learn in this chapter is Euler’s formula for solids:
F – E + V = 2
where F = Faces, E = Edges, and V = Vertices.
This formula helps to quickly check if a solid is drawn correctly.
Use these solutions by studying one topic at a time first reading the theory, then solving examples, and finally practicing all the NCERT questions. Always revise with diagrams and nets to improve 3D imagination. This method helps to perform well in CBSE exams and develop strong geometry skills.