We all have learnt more about the shapes. The various shapes of polygons, triangles, squares etc. here we visualize about them.
Around us there many things and have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth.
That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes.
The 8 corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces.
In 3-D or three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions − length, width and height.
Take a cardboard box. Cut the edges to lay the box flat. You have now a net for that box. A net is a sort of skeleton-outline in 2-D [Fig154 (i)], which, when folded, results in a 3-D shape.
When you draw a solid shape, the images are somewhat distorted to make them appear three-dimensional.
Each face of the piece is a square! We call this face a ‘cross-section’ of the whole bread.
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:
An oblique sketch does not have proportional lengths. Still it conveys all important aspects of the appearance of the solid.
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:
One way is to view by cutting or slicing the shape, which would result in the cross-section of the solid.
Another way is by observing a 2-D shadow of a 3-D shape.
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.