# Find the approximate change in the surface area of a cube of side x meters caused by decreasing the side by 1%

**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 surface area of a cube (S) of side x is given by

S = 6x^{2}

Therefore,

dS = (dS / dx) Δx

= (12 x) Δx

= (12 x) (0.01x)

[∵ 1% of x is 0.01x]

= 0.12x^{2}

Hence,

the approximate change in the surface area of the cube is 0.12x^{2}m^{2}

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.4 Question 5

## Find the approximate change in the surface area of a cube of side x meters caused by decreasing the side by 1%

**Summary:**

The approximate change in the surface area of a cube of side x meters is caused by decreasing the side by 1% is 0.12x^{2}m^{2}

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