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

Last updated at April 16, 2024 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 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
โด 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 ๐ฝ/๐ ๐ when ๐ฅ = 10 cm
We know that
Volume of cube = (Edge)3
V = ๐ฅ3
Differentiate w.r.t time
๐ ๐ฝ/๐ ๐ = (๐ (๐๐))/๐ ๐
๐๐/๐๐ก = (๐(๐ฅ3))/๐๐ก ร ๐๐ฅ/๐๐ฅ
๐๐/๐๐ก = (๐(๐ฅ3))/๐๐ฅ ร ๐๐ฅ/๐๐ก
๐๐/๐๐ก = 3๐ฅ2 . ๐ ๐/๐ ๐
๐๐/๐๐ก = 3๐ฅ2 ร 3
๐๐/๐๐ก = 9๐ฅ2
When ๐ฅ = 10
โ ๐๐/๐๐กโค|_(๐ฅ =10) = 9(10)2
โ ๐๐/๐๐กโค|_(๐ฅ =10) = 900
Since value is in cm3 & time is in sec
๐ ๐ฝ/๐ ๐ = 900 cm3/sec
Hence, volume of a cube is increasing at the rate of 900 cm3/sec

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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