Visualising Solid Shapes Questions and Answers - Free PDF Download
Exercise 13.4
1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).
(a) A ball
Ans: The shape of the shadow of a ball will be a circle.
(b) A cylindrical pipe
Ans: The shape of the shadow of a cylindrical pipe will be a line.
(c) A book
Ans: The shape of the shadow of a book will be a rectangle.
2. Here are the shadows of some 3-D objects, when seen under the lamp of the overhead projector. Identify the solid (s) that match each shadow. (There may be multiple answers for these!)
Ans: Compact disk, Chapatti, Football, Plate. The shadow of these solids are circle.
Ans: A dice, Chalk box, Square paper sheet, cubical magic box.
Ans: Triangular pyramid, Ice-cream cone, Birthday cap
Ans: NoteBook, Table, Geometry Box
3. Examine if the following are true statements:
(i) The cube can cast a shadow in the shape of a rectangle.
Ans: True.
(ii) The cube can cast a shadow in the shape of a hexagon.
Ans: False. A cube can cast shadows only in the shape of a square. Therefore, any other shapes are not possible.
NCERT Solutions for Class 7 Maths Chapter 13 Visualising Solid Shapes Exercise 13.4
Opting for the NCERT solutions for Ex 13.4 Class 7 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 13.4 Class 7 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 7 students who are thorough with all the concepts from the Subject Visualising Solid Shapes textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 7 Maths Chapter 13 Exercise 13.4 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
Besides these NCERT solutions for Class 7 Maths Chapter 13 Exercise 13.4, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.
Do not delay any more. Download the NCERT solutions for Class 7 Maths Chapter 13 Exercise 13.4 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.
Class 7 Maths Chapter 13: Exercises Breakdown
CBSE Class 7 Maths Chapter 13 Other Study Materials
Chapter-Specific NCERT Solutions for Class 7 Maths
Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
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FAQs on NCERT Solutions For Class 7 Maths Chapter 13 Visualising Solid Shapes Exercise 13.4 - 2025-26
1. Where can I find accurate, step-by-step NCERT Solutions for Class 7 Maths Chapter 13, Visualising Solid Shapes?
You can find comprehensive and reliable NCERT Solutions for Class 7 Maths Chapter 13, Visualising Solid Shapes, right here on Vedantu. These solutions are prepared by subject matter experts and are aligned with the latest CBSE 2025-26 syllabus. They provide detailed, step-by-step methods for solving every question in the NCERT textbook, including all exercises.
2. How do the NCERT Solutions explain solving questions from Exercise 13.1 about identifying nets for different 3D shapes?
The NCERT Solutions for Exercise 13.1 guide you on how to solve problems involving nets by:
- Providing a clear method to visualise folding the 2D net.
- Showing which edges will join to form the 3D shape, such as a cube, cuboid, or pyramid.
- Explaining why certain nets will work while others will fail (e.g., by having overlapping faces or gaps).
- Using simple diagrams to illustrate the correct formation of the solid shape from its net.
3. What is the correct method to draw a cuboid using an isometric sketch as per the NCERT Class 7 Maths solutions?
As per the NCERT solutions, the correct method for drawing a cuboid on an isometric dot sheet involves these steps:
- Draw a parallelogram for the front face, keeping the dimensions proportional.
- From each of the four vertices, draw parallel lines backwards. The length of these lines will represent the depth of the cuboid.
- Connect the endpoints of these lines to form the back face, which should be another parallelogram identical to the front one.
- This method ensures all dimensions are kept in proportion, giving a realistic 3D representation.
4. How can I use Euler's formula to solve problems in Chapter 13, and how is it explained in the NCERT solutions?
The NCERT solutions explain Euler's formula, F + V - E = 2 (where F is faces, V is vertices, and E is edges), as a verification tool for polyhedrons. The solutions demonstrate its application by:
- First, guiding you to correctly count the faces, vertices, and edges of a given solid shape.
- Then, substituting these values into the formula.
- If the equation holds true (results in 2), it confirms the shape is a valid polyhedron and your counting is correct. This method is used to solve verification problems in the exercises.
5. What type of problems from Exercise 13.3, involving different views of solid shapes, are solved in the NCERT solutions?
In the NCERT Solutions for Exercise 13.3, you will find step-by-step answers for problems that require you to identify the top, front, and side views of various solid objects. The solutions clearly illustrate how to:
- Draw the 2D representation for each specific view (top, front, side).
- Match given 2D views to the correct 3D solid.
- Understand how the perception of a shape changes based on the viewing angle.
6. Why is an isometric sketch considered a more accurate representation of a 3D object than an oblique sketch in the NCERT textbook?
An isometric sketch is considered more accurate because it maintains the proportional measurements of the actual solid object. In contrast, an oblique sketch is easier to draw but often distorts the object's depth and angles, making the back faces look unrealistic. The NCERT solutions for Chapter 13 emphasise isometric sketches for providing a more realistic and dimensionally correct view of solid shapes.
7. The NCERT solutions show a cube can have multiple nets. How can I logically determine if any given 2D net will correctly fold into a cube?
To determine if a net forms a cube, you must ensure two key conditions are met, a logic often applied in the NCERT solutions. First, the net must consist of exactly six squares. Second, when you mentally fold the net, no two squares should overlap, and there should be no gaps. A common method is to fix one square as the base and visualise folding the other five squares to see if they form the top and the four side faces without conflict.
8. When solving problems about cross-sections, how do the solutions help in visualising the new face created by a vertical or horizontal cut?
The NCERT solutions for Chapter 13 help in visualising cross-sections by explaining the resulting 2D shape logically. For instance, they clarify that a horizontal cut through a cylinder results in a circular cross-section, while a vertical cut produces a rectangular one. The solutions often use simple analogies, like slicing a piece of fruit, to help you understand that the shape of the cut surface (the cross-section) depends entirely on the angle of the slice relative to the solid's orientation.
9. What are common mistakes students make when counting faces, vertices, and edges, and how do the NCERT solutions help avoid them?
A common mistake is double-counting edges or missing hidden faces and vertices in a 2D drawing of a 3D shape. The NCERT solutions help prevent this by encouraging a systematic approach. They guide you to first count the faces, then the vertices (corners where edges meet), and finally the edges connecting the vertices. By following this structured method and using Euler's formula for verification, you can confidently arrive at the correct counts for any polyhedron.
