Visualising Solid Shapes Definition Properties Nets and Solved Examples
When you look around your room or your classroom or any place you go, it is filled with different shapes. Right from the rectangular book which you read last till your glass of milk in the form of a cylinder, shapes are all around us. This is the reason why visualising solid shapes is one of the most important skillsets every one should learn.
It is necessary to teach distinguishing between different shapes and sizes. The healthy collection of tips and notes regarding visualising solid shapes class 8 will help you in your upcoming exams.
Two Dimensional Shapes
For introduction of visualising solid shapes, we will first learn about 2D shapes. Shapes which we can draw on paper or other flat surfaces are called two-dimensional shapes or plane figures. We cannot touch or feel 2D shapes as we can for 3D shapes, which we will learn about later. 2D shapes only have length and width.
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Three Dimensional Shapes
Another vital topic for visualising solid shapes class 8 notes is the concept of 3D shapes, also known as solid figures. Solid figures are usually defined by three dimensions – length, height and width. These figures can be felt by human touch and cannot be drawn on flat surfaces.
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Vertices, Edges and Faces of 3D Figures
In 3D or solid figures for visualisation of solid shapes, faces are the flat 2D surfaces (of any shape) which are joined with lines and points to make solid figures.
Similarly, edges are those line segments at which the faces of solid figures meet.
In contrast, vertices are the points where two or more edges meet.
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Here is a table which will help you in your NCERT solutions for class 8th maths chapter 10 visualising solid shapes.
Did You Know?
Euler’s Formula states that the no. of faces, edges and vertices in a regular shape are related via the formula F + V = E + 2.
Pop Quiz 1
How many faces does a sphere contain?
0
1 (Answer)
Infinite
10
Geometric Nets for 3D Shapes
A very important concept for class 8 visualising solid shapes and class 7 visualising solid shapes is that of geometric nets. Geometric nets are 2D figures which are obtained when a 3D figure is opened up. The net can then be folded back to reconstruct the original 3D figure. For example, take a look at the below figure.
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How to Draw 3D Figures on Flat Surfaces?
There are two ways to draw solid figures on flat surfaces. The process is generally called visual illusion and is required for visualising solid shapes class 8 NCERT solutions and visualising solid shapes class 7 NCERT solutions.
Oblique Sketching
In oblique sketches, even though it seems we have drawn the whole figure, we cannot get the complete view of the figure and the length of all the edges are also not the same. This is a popular area for teachers to ask questions from in NCERT solution of class 7 of maths chapter visualising solid shapes.
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Isometric Sketching
Special sheets called isometric sheets are available upon which dots are constructed to make several equilateral triangles. You can draw 3D figures on such sheets such that the original dimensions of the figure are proportional to the sizes we draw. This process is called isometric sketching and is an important concept for class 8 maths visualising solid shapes.
So, this was all regarding visualising solid shapes, and covers enough for NCERT class 7 maths visualising solid shapes and NCERT class 8 maths visualising solid shapes. To know more about this topic and or any other questions on visualising solid shapes, visit the Vedantu website or download our mobile app today!
FAQs on Visualising Solid Shapes in Three Dimensional Geometry
1. What does visualising solid shapes mean in Maths?
Visualising solid shapes means mentally understanding and interpreting 3D objects from different views and representations. It involves imagining how shapes like cubes, cuboids, cylinders, cones, and spheres look from the front, top, or side. Key skills include:
- Identifying faces, edges, and vertices
- Recognising nets of solid shapes
- Understanding different 2D views of 3D objects
- Counting unit cubes in stacked figures
2. What are the different views of a solid shape?
The different views of a solid shape are the top view, front view, and side view. These views show how a 3D object appears from different directions:
- Top view: How the object looks from above
- Front view: How it looks from the front
- Side view: How it looks from the left or right side
3. How do you identify faces, edges, and vertices of a solid?
Faces, edges, and vertices are identified by examining the flat surfaces, line segments, and corner points of a solid shape. Specifically:
- Face: A flat surface of a solid
- Edge: A line segment where two faces meet
- Vertex: A point where edges meet
4. What is a net of a solid shape?
A net of a solid shape is a 2D pattern that can be folded to form a 3D solid. When laid flat, it shows all the faces connected along their edges. For example:
- A cube net consists of 6 equal squares
- A cylinder net has 1 rectangle and 2 circles
5. How can you count cubes in a 3D stacked figure?
To count cubes in a 3D stacked figure, count cubes layer by layer, including hidden cubes. Follow these steps:
- Count cubes in the bottom layer
- Count cubes in each upper layer
- Add all layers together
6. What is the difference between 2D and 3D shapes?
The main difference between 2D and 3D shapes is that 2D shapes have length and breadth, while 3D shapes have length, breadth, and height. In detail:
- 2D shapes: Flat figures like squares and triangles
- 3D shapes: Solid objects like cubes and spheres
7. How do you draw the top, front, and side views of a solid?
To draw top, front, and side views, sketch how the solid appears from each direction separately. Steps include:
- Look at the object directly from the chosen direction
- Draw only visible outlines
- Ensure correct height, width, and depth proportions
8. Why is visualising solid shapes important?
Visualising solid shapes is important because it develops spatial reasoning and improves understanding of geometry and real-world structures. It helps learners:
- Solve geometry problems accurately
- Interpret diagrams and models
- Understand volume and surface area concepts
- Apply Maths in architecture and engineering
9. What are common mistakes when visualising 3D shapes?
Common mistakes when visualising 3D shapes include ignoring hidden parts and miscounting faces or cubes. Typical errors are:
- Not counting hidden cubes in stacked figures
- Confusing edges with faces
- Drawing incorrect proportions in different views
- Choosing incorrect nets that cannot fold into the solid
10. Can you give an example of visualising a cube from different views?
Yes, a cube looks like a square from the top, front, and side views. Since all faces of a cube are equal squares:
- Top view: Square
- Front view: Square
- Side view: Square
