Page 21 - Mathematics Class - IX

ACTIVITY 2.2

OBJECTIVE

To verify the algebraic identity: (a + b) = a + 3a b + 3ab + b 3
3
2
3
2
MATERIALS REQUIRED
64 unit cubes made of wood (dimension is 1 unit × 1 unit × 1 unit).

PRE-REQUISITE KNOWLEDGE
Concept of volume of an object as the number of unit cubes in it.

THEORY
1. Cuboid: A cuboid is a box-shaped object. It has six flat faces and all angles are right angles. All faces of
cuboid are rectangles.

Matchbox, brick, geometry box, etc. are cuboids. Height

The volume of a cuboid is found using the formula:
Volume = Length × Width × Height Width

Length

2. Cube: A cube is cuboid whose length, breadth and height are equal. It has six flat faces and all angles are
right angles. All faces of cube are squares.

Dice, Rubik’s cube, etc. are cubes.
Side
The volume of a cube is found using the formula:
Volume = (Side) 3
Side
Side
PROCEDURE

1. Take a = 3 and make a cube of dimensions a , i.e. 3 × 3 × 3 using 27 unit cubes as shown in Fig. (a).
3
2. Take b = 1 and make a cuboid of dimensions a b, i.e. 3 × 3 × 1 as shown in Fig. (b). Add this three times
2
in Fig. (a) as shown in Fig. (c).

Fig. (a) Fig. (b) Fig. (c) Fig. (d)

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