# Ex 6.1,4 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

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 the cube increasing when the edge is 10 cm long? Let ๐ฅ 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, ๐๐ฅ๏ทฎ๐๐ก๏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 ๐๐๏ทฎ๐๐ก๏ทฏ when ๐ฅ = 10 cm We know that Volume of cube = (edge)3 V = ๐ฅ3 Differentiate w.r.t time ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = ๐(๐ฅ3)๏ทฎ๐๐ก๏ทฏ ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = ๐(๐ฅ3)๏ทฎ๐๐ก๏ทฏ ร ๐๐ฅ๏ทฎ๐๐ฅ๏ทฏ ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = ๐(๐ฅ3)๏ทฎ๐ ๐ฅ๏ทฏ ร ๐๐ฅ๏ทฎ๐๐ก๏ทฏ ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = 3x2 . ๐ ๐๏ทฎ๐ ๐๏ทฏ ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = 3๐ฅ2 ร 3 ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = 9๐ฅ2 When ๐ฅ = 10 ๐๐ฃ๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ฅ =10๏ทฏ = 9(10)2 ๐๐ฃ๏ทฎ๐๐ก๏ทฏ๏ทฏ๏ทฎ๐ฅ =10๏ทฏ = 900 Since value is in cm3 & time is in sec ๐๐ฃ๏ทฎ๐๐ก๏ทฏ = 900 ๐ ๐๏ทฎ3๏ทฏ๏ทฎ๐ ๐๐๏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

Chapter 6 Class 12 Application of Derivatives

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.