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Example 24 - Find approx change in volume V of a cube of side x

Example 24 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Question 11 Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.Given Side of the cube = x metres Also, Increase in side = 2% of side = 0.02x Hence, โˆ†๐’™ = 0.02 x And, Volume of the cube = V = x3 m3 We need to find Approximate change in volume of the cube i.e. โˆ†๐‘ฝ Now, โˆ†๐‘‰ = ๐‘‘๐‘‰/๐‘‘๐‘ฅ โˆ†๐‘ฅ" " = (๐‘‘(๐‘ฅ^3))/๐‘‘๐‘ฅ โˆ†๐‘ฅ" " = 3x2 (0.02x) = 0.06 x3 Hence, the approximate change in the volume of the cube is 0.06 x3 m3

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.