Misc 19 - A cylindrical tank of radius 10 m being filled wheat

Misc. 19 - Chapter 6 Class 12 Application of Derivatives - Part 2
Misc. 19 - Chapter 6 Class 12 Application of Derivatives - Part 3

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

Transcript

Misc. 19 A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic meter per hour. Then the depth of the wheat is increasing at the rate of (A) 1 m /h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/hLet r be the radius of cylindrical tank & V be the volume of cylindrical tank & h be the depth of the cylindrical tank Given that cylindrical tank of radius 10 m being filled with wheat at the rate of 314 cubic meter per hour i.e. Change if volume of tank is 314 m3/hr. when r = 10 i.e. ๐’…๐‘ฝ/๐’…๐’• = 314 m3/hr. when r = 10 We need to find at what rate depth is increasing i.e. we need to find ๐’…๐’‰/๐’…๐’• Now, ๐‘‘๐‘‰/๐‘‘๐‘ก = 314 (๐‘‘ (๐œ‹๐‘Ÿ^2 โ„Ž))/๐‘‘๐‘ก = 314 (๐‘‘(๐œ‹(102)โ„Ž))/๐‘‘๐‘ก = 314 (๐‘‘(100๐œ‹โ„Ž))/๐‘‘๐‘ก = 314 100๐œ‹ ๐’…๐’‰/๐’…๐’• = 314 ๐‘‘โ„Ž/๐‘‘๐‘ก = 314/100๐œ‹ ๐‘‘โ„Ž/๐‘‘๐‘ก = 314/(100 ร— 3.14) ๐‘‘โ„Ž/๐‘‘๐‘ก = 314/314 ๐‘‘โ„Ž/๐‘‘๐‘ก = 1 Since depth is in meter & time is in hr So, ๐’…๐’‰/๐’…๐’• = 1 m/hr. So, A is the correct answer.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.