Check sibling questions

Ex 6.1, 4 - An edge of a variable cube is increasing at 3 cm/s

Ex 6.1,4 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,4 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Transcript

Ex 6.1, 4 An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of cube increasing when the edge is 10 cm long?Let ๐’™ be the edge of cube. & V be the volume of cube. Given that Edge of cube is increasing at the rate of 3 cm/ sec โˆด ๐’…๐’™/๐’…๐’• = 3 cm/sec We need to calculate how fast volume of cube increasing when edge is 10 cm i.e. we need to find ๐’…๐‘ฝ/๐’…๐’• when ๐‘ฅ = 10 cm We know that Volume of cube = (Edge)3 V = ๐‘ฅ3 Differentiate w.r.t time ๐’…๐‘ฝ/๐’…๐’• = (๐’…(๐’™๐Ÿ‘))/๐’…๐’• ๐‘‘๐‘‰/๐‘‘๐‘ก = (๐‘‘(๐‘ฅ3))/๐‘‘๐‘ก ร— ๐‘‘๐‘ฅ/๐‘‘๐‘ฅ ๐‘‘๐‘‰/๐‘‘๐‘ก = (๐‘‘(๐‘ฅ3))/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ฅ/๐‘‘๐‘ก ๐‘‘๐‘‰/๐‘‘๐‘ก = 3๐‘ฅ2 . ๐’…๐’™/๐’…๐’• ๐‘‘๐‘‰/๐‘‘๐‘ก = 3๐‘ฅ2 ร— 3 ๐‘‘๐‘‰/๐‘‘๐‘ก = 9๐‘ฅ2 When ๐‘ฅ = 10 โ”œ ๐‘‘๐‘‰/๐‘‘๐‘กโ”ค|_(๐‘ฅ =10) = 9(10)2 โ”œ ๐‘‘๐‘‰/๐‘‘๐‘กโ”ค|_(๐‘ฅ =10) = 900 Since value is in cm3 & time is in sec ๐’…๐‘ฝ/๐’…๐’• = 900 cm3/sec Hence, volume of a cube is increasing at the rate of 900 cm3/sec

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.