Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise


Ex 6.1, 9 A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.Since Balloon is spherical Let r be the radius of balloon . & V be the volume of balloon. We need to find rate at which balloon volume is increasing when radius is 10cm i.e. We need to find change of volume w.r.t radius when r = 10 i.e. we need to find ๐’…๐‘ฝ/๐’…๐’“ when r = 10 cm We know that Volume of sphere = V = 4/3 ฯ€r3 Now, ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = (๐‘‘ (4/3 ๐œ‹๐‘Ÿ3))/๐‘‘๐‘Ÿ ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 4/3 ฯ€ ๐‘‘(๐‘Ÿ3)/๐‘‘๐‘Ÿ ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 4/3 ฯ€ 3๐‘Ÿ^2 ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 4๐œ‹๐‘Ÿ^2 When r = 10 ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 4 ร— ฯ€ ร— (10)2 ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 400ฯ€ Since volume is in cm3 & Radius is in cm So, ๐‘‘๐‘‰/๐‘‘๐‘Ÿ = 400ฯ€ cm3/cm Hence, volume is increasing at the rate of 400 ฯ€ cm3/cm when r = 10 cm

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.