Find the approximate change in the volume V of a cube of side x meters – InterviewSolution

1.

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

Answer»

We have; V = x³ and ∆x = 1% of x= 0.01x

dv = \(\frac{dV}{dx}\)∆x = 3x²∆x

= 3x² × 0.01x = 0.03x³ = 0.03V

⇒ \(\frac{dV}{V}\) = 0.03

Therefore 3% is the approximate increase in volume.

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