Page 213 - Maths Skills - 7

Visualising Solid Shapes 211

INTRODUCTION
In our daily life, we see several objects around us. We find they may have different shapes and sizes, but yet
they may have a common feature in term of different dimensions. We know a line has only one dimension i.e.,
its length. Figures like currency note, postage stamp, postcard, etc. are examples of plane figures. They have two
dimensions i.e., length and breadth. On the other hand objects like matchbox, book, ball, drum etc. are examples
of solid shapes having three dimensions i.e., length, breadth and height.

SPECIMEN

A line Currency note Matchbox
One-dimensional figure Two-dimensional figure Three-dimensional figure

Note: We write 2D for 2-dimensional figures and 3D for 3-dimensional objects.
We will study how to draw 3D solids in 2D surface. Observe few common objects shown in Figure.

SPRITE CAKE

MYSTIQUE TISSUE CHOCOLATE

If you observe them carefully, they are all three-dimensional solids represented on two-dimensional surface of
paper. Can you draw them yourself? Let us see how we can represent a 3D object on 2D surfaces.

DRAWING SOLIDS ON A FLAT SURFACE
We often need to draw solids an a paper in geometry, it is easier to make the representations on a 2D plane by
using the following methods:

Oblique Sketches of Cube
Take a square grid paper and draw a square as shown in Fig. 1. Name it as ABCD.

Fig. 1 Fig. 2 Fig. 3 Fig. 4

Draw another square EFGH with equal length as shown in Fig. 2. Join AE, DH, BF and CG as shown in Fig. 3.
You may show that edges EF, BF and GF as dotted line as these are the hidden edges when represented in 2D.

A cube when drawn without a square grid paper will look like as shown in Fig. 4. A cube has 8 vertices, 6 faces
and 12 edges.

Oblique Sketches of Cuboid
To represent a cuboid on a square grid paper, draw a rectangle PQRS on it as shown in Fig. 5. Draw another
rectangle of same dimension and name it as TUVW as shown in Fig. 6. Now, join PT, QU, SW and RV to get a