1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise


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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.