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activity 10 lab manual class 9 cbse

Answers

Answered by shraddhagulve1234

OBJECTIVE

To verify the algebraic identity a³-b³ = (a-b) (a²+ab+b²).

Concept cuboid and its volume.

Concept of cube and its volume.

Theory

For concept of cuboid and its volume refer to Activity 7.

For concept of cube and its volume refer to Activity 7.

Procedure

Using acrylic sheet, make a cuboid of dimensions (a – b) x a x a, where b < a. (see Fig. 10.1)

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 1

Using acrylic sheet, make another cuboid of dimensions (a-b) x a x b, where b < a. (see Fig. 10.2).

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 2

Now, make one more cuboid of dimensions (a-b) x b x b. (see Fig. 10.3)

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 3

Now, make a cube of dimensions b x b x b. (see Fig. 10.4)

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 4

Arrange the cube and cuboids obtained in Fig. 10.1 to 10.4 to form a solid as shown in Fig. 10.5, which is a cube of side a units.

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 5

Now, remove a cube of side b units from the solid obtained in Fig. 10.5, thus we obtain solid as shown in Fig. 10.6.

NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) 6

Demonstration

For Fig. 10.1, volume of cuboid = (a-b) x a x a = (a-b)a²

For Fig. 10.2, volume of cuboid = (a-b) x a x b = (a-b)ab

For Fig. 10.3, volume of cuboid = (a – b) x b x b = (a – b)b²

For Fig. 10.4, volume of cube =b³

For Fig. 10.5, volume of cube = Sum of volume of all cubes and cuboids

= (a – b)a² + (a – b)ab + (a – b)b² + b³ …..(i)

The cube obtained in Fig. 10.5 has its each side a.

Its volume = (side)³ = a³ …..(ii)

From Eqs. (i) and (ii), we get

a³ = (a – b)a² + (a – b)ab + (a – b)b² + b³ …..(iii)

For Fig. 10.6, volume of solid obtained = a³ – b³

= (a – b)a² + (a – b)ab + (a – b)b² + b³ – b³ [from Eq.(iii)]

= (a – b)a² + (a – b)ab + (a – b)b² = (a-b) (a² +ab + b²)

Therefore, a³-b³ = (a-b) (a²+ab+b²)

Here, volume is in cubic units.

Observation

On actual measurement, we get

a = ……. , b = ……. ,

So, a² =…….. , b² = ……. ,

(a- b) = ……. , ab = ……. ,

a³ =…….. , b³ = ……. ,

Hence, a³-b³ = (a-b) (a²+ab+b²).

Result

The algebraic identity a³-b³ = (a-b) (a²+ab+b²) has been verified.

NCERT Class 9 Maths Lab Manual – Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²)