Class 7 Notes - Visualising Solid Shapes

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Visualising Solid Shapes

In this chapter, students will learn to understand and visualize three-dimensional (3-D) shapes, their properties, and how they relate to two-dimensional (2-D) representations. This is an important skill for geometry, engineering, and real-life problem solving.

1. Introduction to Solid Shapes

  • Solid shapes are three-dimensional objects that have length, breadth, and height.
  • Examples: Cube, Cuboid, Sphere, Cylinder, Cone, Pyramid, Prism.

2. Faces, Edges, and Vertices

  • Face: A flat or curved surface of a solid shape.
  • Edge: A line segment where two faces meet.
  • Vertex (Vertices): A point where edges meet.
Shape Faces Edges Vertices
Cube 6 12 8
Cuboid 6 12 8
Sphere 1 (curved) 0 0
Cylinder 3 (2 flat, 1 curved) 2 0
Cone 2 (1 flat, 1 curved) 1 1

3. Nets of 3-D Shapes

A net is a two-dimensional (2-D) figure that can be folded to form a 3-D solid. Nets help us understand the surfaces of solids.

  • Cube net: 6 squares arranged so they can be folded into a cube.
  • Cuboid net: 6 rectangles.
  • Cylinder net: 2 circles and 1 rectangle.
Activity: Draw and cut out nets for a cube and a cylinder. Fold them to make the solids.

4. Views of 3-D Shapes

  • Top View: Looking at the object from above.
  • Front View: Looking at the object from the front.
  • Side View: Looking at the object from the side.

Different views help us understand the structure of solids. For example, a cylinder looks like a rectangle from the side and a circle from the top.

5. Drawing Solids on a Flat Surface

  • Isometric sketches: Drawings that show 3-D objects on 2-D paper using parallel lines.
  • Oblique sketches: Drawings where the front face is drawn in true shape and the other faces are drawn at an angle.
Try it: Draw a cube using isometric dot paper.

6. Mapping Space Around Us

  • Maps and floor plans are 2-D representations of 3-D spaces.
  • Understanding directions (left, right, front, back) is important for reading maps.

7. Word Problems

  1. How many faces does a cuboid have? 6
  2. Which solid shape has only one curved surface and no edges? Sphere
  3. Draw the net of a cylinder. How many faces does it have?
  4. What is the difference between a cube and a cuboid?

8. Summary

  • Solid shapes have faces, edges, and vertices.
  • Nets help us visualize and construct 3-D shapes.
  • Different views (top, front, side) help us understand solids.
  • Drawing and mapping are useful skills for geometry and real life.