The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
(A) 0.06x³m³  (B) 0.6x³m³  (C) 0.09x³m³  (D)0.9x³m³

Solution:

We can use differentials to calculate small changes in the dependent variable of a function corresponding to small changes in the independent variable

The volume of a cube (V) of side x is given by

V = x³.

Therefore,

Change in volume can be written as:

dV = (dV / dx) Δx

= (3x²) (0.03x)

[ Since 3% of x is 0.03x ]

On simplifying the value, we get

= 0.09x³

Hence, the approximate change in the volume of the cube is 0.09 x³m³.

Thus, the correct option is C

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.4 Question 9

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is. (A) 0.06x³m³ (B) 0.6x³m³ (C) 0.09x³m³ (D) 0.9x³m³

Summary:

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is 0.09 x³m³. Thus, the correct option is C