Visualising Solid Shapes - Revision Notes

 CBSE Class–VII Subject Mathematics

Revision Notes
Chapter –15
Visualising Solid Shapes

  • The circle, the square, the rectangle, the quadrilateral and the triangle are examples of plane figures; the cube, the cuboid, the sphere, the cylinder, the cone and the pyramid are examples of solid shapes.
  • Plane figures are of two-dimensions (2-D) and the solid shapes are of three-dimensions (3-D).
  • The corners of a solid shape are called its vertices; the line segments of its skeleton are its edges; and its flat surfaces are its faces.
  • A net is a skeleton-outline of a solid that can be folded to make it.  The same solid can have several types of nets.
  • Solid shapes can be drawn on a flat surface (like paper) realistically. We call this 2-D representation of a 3-D solid.
  • Two types of sketches of a solid are possible:
    (a) An oblique sketch does not have proportional lengths. Still it conveys all important aspects of the appearance of the solid.
    (b) An  isometric sketch is drawn on an isometric dot paper, a sample of which is given at the end of this book.  In an isometric sketch of the solid the measurements kept proportional.
  • Visualising solid shapes is a very useful skill.  You should be able to see ‘hidden’ parts of the solid shape.
  • Different sections of a solid can be viewed in many ways:
    (a) One way is to view by cutting or slicing the shape, which would result in the cross-section of the solid.
    (b) Another way is by observing a 2-D shadow of a 3-D shape.
    (c) A third way is to look at the shape from different angles; the front-view, the side-view and the top view can provide a lot of information about the shape observed.