Slide9.JPG

Slide10.JPG

Subscribe to our Youtube Channel - https://you.tube/teachoo

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

Transcript

Ex 6.1, 13 A balloon, which always remains spherical, has a variable diameter 3/2 (2๐‘ฅ +1). Find the rate of change of its volume with respect to ๐‘ฅ. Let d be the diameter of the balloon Given d = 3/2 (2x + 1) Let r be the radius of the balloon r = ๐‘‘/2 = 3/4 (2x + 1) The balloon is a sphere Volume of the balloon = Volume of sphere = 4/3 ๐œ‹๐‘Ÿ^3 We need to find rate of change of volume with respect to x that is ๐‘‘๐‘ฃ/๐‘‘๐‘ฅ ๐‘‘๐‘ฃ/๐‘‘๐‘ฅ = ๐‘‘/๐‘‘๐‘ฅ (4/3 ๐œ‹๐‘Ÿ^3 ) = 4๐œ‹/3 (๐‘‘๐‘Ÿ^3)/๐‘‘๐‘ฅ = 4๐œ‹/3 ๐‘‘/๐‘‘๐‘ฅ (27/64 (2๐‘ฅ+1)^3 ) = 9๐œ‹/16 (๐‘‘(2๐‘ฅ + 1)^3)/๐‘‘๐‘ฅ = 9๐œ‹/16 3(2x + 1)2 (2) = ๐Ÿ๐Ÿ•๐…/๐Ÿ– (๐Ÿ๐’™+๐Ÿ)^๐Ÿ Hence, ๐‘‘๐‘ฃ/๐‘‘๐‘ฅ = 27๐œ‹/8 (2๐‘ฅ+1)^2

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.