# Misc. 19 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

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 m3 /h (B) 0.1 m3 /h (C) 1.1 m3 /h (D) 0.5 m3 /h Let 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 10m 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. 𝑑𝑉𝑑𝑡 = 314 m3/hr. when r = 10 We need to find at what rate depth is increasing i.e. we need to find 𝑑ℎ𝑑𝑡 We know that Volume of cylindrical tank = πr2h, & Given 𝑑𝑉𝑑𝑡 = 314 m3/hr. when r = 10 𝑑𝑉𝑑𝑡 = 314 𝑑 𝜋𝑟2ℎ𝑑𝑡 = 314 𝑑(𝜋102ℎ)𝑑𝑡 = 314 𝑑(100𝜋ℎ)𝑑𝑡 = 314 100 𝜋 𝑑(ℎ)𝑑𝑡 = 314 𝑑ℎ𝑑𝑡 = 314100𝜋 𝑑ℎ𝑑𝑡 = 314100 × 3.14 𝑑ℎ𝑑𝑡 = 314314 𝑑ℎ𝑑𝑡 = 1 Since depth is in meter & time is in hr So, 𝑑ℎ𝑑𝑡 = 1m/hr. Thus, The depth of the tank change at 1m /hour So, A is the correct answer.

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 9 years. He provides courses for Maths and Science at Teachoo.