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Finding rate of change
Ex 6.1, 1
Ex 6.1,17 (MCQ)
Example 5
Ex 6.1,15 Important
Example 6
Ex 6.1,16
Ex 6.1, 18 (MCQ) Important
Example 2
Ex 6.1,2
Example 35
Example 3
Ex 6.1,5 Important
Ex 6.1,3
Ex 6.1,6
Ex 6.1,12
Ex 6.1,13 Important
Misc 16 (MCQ) You are here
Ex 6.1,14
Example 31 Important
Ex 6.1,4 Important
Example 30 Important
Example 4 Important
Ex 6.1,7
Ex 6.1,8
Ex 6.1,9
Ex 6.1,11 Important
Misc 2 Important
Ex 6.1,10 Important
Example 32 Important
Finding rate of change
Last updated at May 29, 2023 by Teachoo
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.