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 = 6x²

Therefore,

dS = (dS / dx) Δx

= (12 x) Δx

= (12 x) (0.01x)

[∵ 1% of x is 0.01x]

= 0.12x²

Hence,

the approximate change in the surface area of the cube is 0.12x²m²

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 0.12x²m²