Ex 6.1

Chapter 6 Class 12 Application of Derivatives
Serial order wise

### 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 โด 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))/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 ๐๐/๐๐กโค|_(๐ฅ =10) = 9(10)2 โ 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