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

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  1. Chapter 6 Class 12 Application of Derivatives
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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 the cube increasing when the edge is 10 cm long? Let ๐‘ฅ 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 Thus, ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ก๏ทฏ = 3cm/sec We need to calculate How fast volume of cube increasing w. r. t time when edge is 10 cm i.e. we need to calculate ๐‘‘๐‘‰๏ทฎ๐‘‘๐‘ก๏ทฏ when ๐‘ฅ = 10 cm We know that Volume of cube = (edge)3 V = ๐‘ฅ3 Differentiate w.r.t time ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = ๐‘‘(๐‘ฅ3)๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = ๐‘‘(๐‘ฅ3)๏ทฎ๐‘‘๐‘ก๏ทฏ ร— ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = ๐‘‘(๐‘ฅ3)๏ทฎ๐‘ ๐‘ฅ๏ทฏ ร— ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = 3x2 . ๐’…๐’™๏ทฎ๐’…๐’•๏ทฏ ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = 3๐‘ฅ2 ร— 3 ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = 9๐‘ฅ2 When ๐‘ฅ = 10 ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฏ๏ทฎ๐‘ฅ =10๏ทฏ = 9(10)2 ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฏ๏ทฎ๐‘ฅ =10๏ทฏ = 900 Since value is in cm3 & time is in sec ๐‘‘๐‘ฃ๏ทฎ๐‘‘๐‘ก๏ทฏ = 900 ๐‘ ๐‘š๏ทฎ3๏ทฏ๏ทฎ๐‘ ๐‘’๐‘๏ทฏ ๐’…๐’—๏ทฎ๐’…๐’•๏ทฏ = 900 cm3/sec Hence, volume of a cube is increasing at the rate of 900 cm3/sec when edge is 10cm

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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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