Find the approximate change in the volume V of a cube of side x meters caused by increasing 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 volume of a cube V of side x is given by

V = x³

Change in volume can be written as dV.

Therefore,

dV = (dV / dx) Δx

= (3x²) Δx

= (3x²)(0.01x)

[∵ 1% of x is 0.01x]

= 0.03 x³

Hence, the approximate change in the volume of the cube is 0.03x³m³

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.4 Question 4

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 1%

Summary:

The approximate change in volume of a cube of side x meters is caused by increasing the side by 1%. We can use differentials to calculate small changes in the dependent variable of a function corresponding to small changes in the independent variable