# The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

(A) 0.06x^{3}m^{3 }(B) 0.6x^{3}m^{3 }(C) 0.09x^{3}m^{3 }(D)0.9x^{3}m^{3}

**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 = x^{3}.

Therefore,

Change in volume can be written as:

dV = (dV / dx) Δx

= (3x^{2}) (0.03x)

[ Since 3% of x is 0.03x ]

On simplifying the value, we get

= 0.09x^{3}

Hence, the approximate change in the volume of the cube is 0.09 x^{3}m^{3}.

Thus, the correct option is C

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) 0.06x^{3}m^{3 }(B) 0.6x^{3}m^{3 }(C) 0.09x^{3}m^{3 }(D) 0.9x^{3}m^{3}

**Summary:**

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

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