Mathematics Class 8 - Visualising Solid-Shapes Notes

Visualising Solid Shapes

Welcome to the chapter on Visualising Solid Shapes for Class 8. In this chapter, you will learn how to understand and represent three-dimensional shapes, identify their faces, edges, and vertices, and draw their nets and views. By the end of this chapter, you will be able to visualize and work with solid shapes confidently!

Introduction

Solid shapes are three-dimensional objects that have length, breadth, and height. Unlike flat shapes (2D), solid shapes (3D) occupy space and can be seen from different angles.

Types of Solid Shapes

• Cuboid: Has 6 rectangular faces, 12 edges, and 8 vertices.
• Cube: All faces are squares; has 6 faces, 12 edges, and 8 vertices.
• Cylinder: Has 2 circular faces and 1 curved surface.
• Sphere: Has only one curved surface and no edges or vertices.
• Cone: Has 1 circular face, 1 curved surface, and 1 vertex.
• Pyramid: Has a polygonal base and triangular faces meeting at a vertex.

Faces, Edges, and Vertices

• Face: A flat or curved surface of a solid shape.
• Edge: A line where two faces meet.
• Vertex: A point where edges meet.

Example: A cuboid has 6 faces, 12 edges, and 8 vertices.

Nets of Solid Shapes

A net is a two-dimensional figure that can be folded to form a three-dimensional solid shape. Nets help us understand the structure of solids.

• Net of a cube: 6 squares arranged so they can be folded into a cube.
• Net of a cuboid: 6 rectangles arranged to form a cuboid.
• Net of a cylinder: 2 circles and 1 rectangle.

Views of Solid Shapes

Solid shapes can be seen from different views:

• Top view (looking from above)
• Front view (looking from the front)
• Side view (looking from the side)

These views help us understand the shape and structure of solids.

Fun Activity: Make Your Own Net!

Draw and cut out the net of a cube or cuboid on paper. Fold it to make the solid shape!

Summary

• Solid shapes have faces, edges, and vertices.
• Nets help us visualize and construct solid shapes.
• Views show how a solid looks from different directions.

Practice Questions

1. How many faces does a cube have?
2. What is the net of a cylinder made of?
3. Name a solid shape with only one curved surface.
4. Draw the top, front, and side views of a cuboid.
5. How many edges does a pyramid with a square base have?

Challenge Yourself

• Make a model of a cube using cardboard and label its faces, edges, and vertices.
• Find objects at home that are shaped like a cylinder, sphere, or cone.

Did You Know?

• Dice are cubes and cans are cylinders!
• The Great Pyramid of Giza is a real-life example of a pyramid shape.

Glossary

• Solid Shape: A three-dimensional object.
• Net: A flat pattern that can be folded into a solid shape.
• Face: A flat or curved surface of a solid.
• Edge: A line where two faces meet.
• Vertex: A point where edges meet.

Answers to Practice Questions

1. 6
2. 2 circles and 1 rectangle
3. Sphere
4. (Student should draw the views)
5. 8

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Practice visualising solid shapes to become a geometry expert!