Question 5 - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

Ex 6.4, 5 - Find approx change in surface area of cube of side x

Ex 6.4,5 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Question 5 Find the approximate change in the surface area of a cube of side x meters caused by decreasing the side by 1%.Let side of the cube = x meters. Given Decrease in side = 1% = − 0.01 x Hence, ∆ x = −0.01 x Surface area of the cube = S = 6x2 m2 We need to find the approximate change in the surface area of the cube i.e. ∆ S Now, ∆ S = 𝑑𝑠/𝑑𝑥 ∆x = 𝑑(6𝑥^2 )/𝑑𝑥 ∆x = 12x (−0.01x) = − 0.12x2 Hence, the approximate change is 0.12x2 m2

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