# Ex 6.1,13 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 6.1,13 A balloon, which always remains spherical, has a variable diameter 32 (2𝑥 +1). Find the rate of change of its volume with respect to 𝑥. Let d be the diameter of the balloon Given d = 32 (2x + 1) Let r be the radius of the balloon r = 𝑑2 = 34 (2x + 1) The balloon is a sphere volume of the balloon = volume of sphere = 43𝜋 𝑟3 We need to find rate of change of volume with respect to x that is 𝑑𝑣𝑑𝑥 𝑑𝑣𝑑𝑥 = 𝑑𝑑𝑥 43𝜋 𝑟3 = 4𝜋3 𝑑 𝑟3𝑑𝑥 = 4𝜋3 𝑑𝑑𝑥 2764 2𝑥+13 = 9𝜋16 𝑑𝑑𝑥 2𝑥+13 = 9𝜋16 3(2x + 1)2 (2) = 𝟐𝟕𝝅𝟖 𝟐𝒙+𝟏𝟐 Hence, 𝑑𝑣𝑑𝑥 = 27𝜋8 2𝑥+12

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.