Last updated at April 19, 2021 by Teachoo

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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 ๐ฝ/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, ๐๐/๐๐ก = 314 (๐ (๐๐^2 โ))/๐๐ก = 314 (๐(๐(102)โ))/๐๐ก = 314 (๐(100๐โ))/๐๐ก = 314 100๐ ๐ ๐/๐ ๐ = 314 ๐โ/๐๐ก = 314/100๐ ๐โ/๐๐ก = 314/(100 ร 3.14) ๐โ/๐๐ก = 314/314 ๐โ/๐๐ก = 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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Chapter 6 Class 12 Application of Derivatives (Term 1)

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About the Author

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.