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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
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