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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

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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. 𝒅𝑽/𝒅𝒕 = 314 m3/hr. when r = 10 We need to find at what rate depth is increasing i.e. we need to find 𝒅𝒉/𝒅𝒕 Now, 𝑑𝑉/𝑑𝑡 = 314 (𝑑 (𝜋𝑟^2 ℎ))/𝑑𝑡 = 314 (𝑑(𝜋(102)ℎ))/𝑑𝑡 = 314 (𝑑(100𝜋ℎ))/𝑑𝑡 = 314 100𝜋 𝒅𝒉/𝒅𝒕 = 314 𝑑ℎ/𝑑𝑡 = 314/100𝜋 𝑑ℎ/𝑑𝑡 = 314/(100 × 3.14) 𝑑ℎ/𝑑𝑡 = 314/314 𝑑ℎ/𝑑𝑡 = 1 Since depth is in meter & time is in hr So, 𝒅𝒉/𝒅𝒕 = 1 m/hr. So, A is the correct answer.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.