How to Identify and Draw Different Solid Shapes in Maths
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: Understanding 2D and 3D Geometry
1. What is the main difference between two-dimensional (2D) and three-dimensional (3D) shapes?
The main difference lies in their dimensions. A two-dimensional (2D) shape, such as a square or a circle, is flat and possesses only two dimensions: length and width. It can be drawn on paper without any depth. In contrast, a three-dimensional (3D) shape, like a cube or a sphere, has three dimensions: length, width, and height (or depth). These are solid objects that occupy space. You can think of a 2D shape as a single face of a 3D object.
2. What does 'visualising solid shapes' actually mean in geometry?
'Visualising solid shapes' is the skill of mentally picturing and understanding a three-dimensional object and its properties, even when it is represented on a two-dimensional surface like a screen or paper. It involves several key techniques, such as:
- Understanding how a 3D object appears from different viewpoints (top, front, and side).
- Drawing 3D objects on a flat surface using methods like oblique and isometric sketches.
- Imagining the 2D shape (cross-section) that would be formed if you were to slice through a solid.
3. What are the key features of an oblique sketch, and how is it used to draw 3D objects?
An oblique sketch is a simple method for drawing a 3D object on a 2D surface. Its key features are:
- The front face of the object is drawn true to its actual shape and size.
- The lines that represent the object's depth, known as receding lines, are drawn at an angle, typically 45 degrees from the horizontal.
- The measurements along the depth axis are often not drawn to scale, and can be shortened to create a more realistic look.
4. How does an isometric sketch represent a 3D object, and what makes it different from an oblique sketch?
An isometric sketch represents a 3D object more accurately by drawing it on special isometric dot paper, where all three dimensions (length, width, and height) are shown to a consistent scale. The primary differences from an oblique sketch are:
- Angles: In an isometric drawing, vertical lines remain vertical, but all horizontal lines are drawn at 30 degrees to the baseline. This creates a realistic corner-view perspective.
- Measurements: All edges are drawn to their true proportional lengths, maintaining the object's scale accurately. In contrast, an oblique sketch only shows the front face in its true shape and often distorts the depth dimension.
5. What are 'nets' in the context of solid shapes, and can any flat arrangement of shapes form a net?
A net is a 2D pattern of flat shapes that can be folded along its edges to create a 3D solid without any overlaps. For example, the net for a cube is made of six connected squares. However, not just any arrangement of the required shapes can form a valid net. The positioning is crucial. For example, six squares arranged in a single long row cannot be folded to form a cube. The shapes must be arranged so that when folded, they correctly form all the faces and vertices of the solid.
6. Explain the importance of faces, edges, and vertices with an example like a cuboid.
Faces, edges, and vertices are the fundamental components that define any polyhedron (a 3D shape with flat faces). Using a cuboid as an example:
- Faces: These are the flat surfaces of the solid. A cuboid has 6 rectangular faces.
- Edges: These are the line segments where two faces meet. A cuboid has 12 edges.
- Vertices: These are the corner points where three or more edges meet. A cuboid has 8 vertices.
7. Why is learning to visualise 3D shapes from 2D drawings a useful skill outside of maths class?
Learning to visualise 3D shapes is a crucial skill with many real-world applications beyond academics. Its importance is seen in various fields:
- Engineering and Architecture: Professionals must interpret 2D blueprints to visualise the 3D building, machine, or structure they represent.
- Design and Gaming: Product designers, graphic artists, and game developers create 2D sketches to plan and visualise 3D models before building them digitally.
- Everyday Life: The skill helps in practical tasks like assembling flat-pack furniture from 2D instructions, understanding maps for navigation, or picturing how object parts fit together.
