NCERT Notes: Grade 8 Maths - Chapter 10: Visualising Solid Shapes

Introduction

The universe isn’t limited to flat, two-dimensional spaces. It expands into the third dimension, introducing us to a plethora of solid shapes. This chapter delves deep into the world of 3D, ensuring that we not only understand these shapes but also visualize and appreciate their presence in our surroundings.

1. Perspective: 2D vs. 3D

• Two-dimensional (2D) shapes: These have length and breadth but lack depth (e.g., square, circle).

• Three-dimensional (3D) shapes: These have length, breadth, and depth, giving them volume (e.g., cube, sphere).

2. Common Solid Shapes

2.1 Cube

• Six identical square faces.
• 12 equal edges.
• 8 vertices.

2.2 Cuboid (Rectangular Prism)

• Opposite faces are identical and parallel.
• 12 edges.
• 8 vertices.

2.3 Cylinder

• Two parallel circular bases.
• A curved surface connecting the bases.

2.4 Cone

• A flat circular base.
• A curved surface that narrows to a point called the vertex.

2.5 Sphere

• Completely round.
• Every point on its surface is equidistant from its center.

2.6 Pyramid

• A polygon base.
• Triangular faces that converge to a common point.

3. Nets of 3D Shapes

A ‘net’ is a 2D shape that can be folded to form a 3D shape. For example, the net of a cube consists of 6 squares connected in a specific arrangement.

4. Viewing Different Sections: Cross-Sections

When a solid is cut by a plane, the shape obtained on the plane is called a cross-section. For example, when a cylinder is cut by a plane parallel to its base, the cross-section is a circle.

5. Mapping Space Around Us

5.1 Oblique Sketch

A sketch that gives a clear idea of the height, width, and depth of an object. It doesn’t have specific scales for different dimensions, but gives a general representation.

5.2 Isometric Sketch

It uses isometric dot paper to represent 3D objects. All dimensions are equally scaled, and angles between them are 120°.

6. Polyhedron

A solid bounded by polygons is called a polyhedron. They don’t have any curved surfaces. Examples include cubes and pyramids.

6.1 Faces, Edges, and Vertices

For any polyhedron:

[ F + V = E + 2 ]

Where: F = Number of faces V = Number of vertices E = Number of edges

7. Euler’s Formula

For any convex polyhedron, the relation between the number of vertices (V), faces (F), and edges (E) is given by Euler’s Formula:

[ F + V - E = 2 ]

Conclusion

Visualizing solid shapes enriches our spatial understanding and is crucial in numerous real-world applications, from architecture to design. This chapter not only imparts knowledge about different 3D shapes but also ensures we appreciate their geometric beauty and significance in the world around us.

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Reference: NCERT Grade 8 Maths - Chapter 10: Visualising Solid Shapes

Note: This article offers an SEO-optimized summary of the concepts related to visualizing solid shapes. For a comprehensive study and in-depth exercises, students should refer to the original NCERT textbook.