

Finding rate of change
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Finding rate of change
Last updated at Aug. 9, 2021 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. π π½/π π = 314 m3/hr. when r = 10 We need to find at what rate depth is increasing i.e. we need to find π π/π π Now, ππ/ππ‘ = 314 (π (ππ^2 β))/ππ‘ = 314 (π(π(102)β))/ππ‘ = 314 (π(100πβ))/ππ‘ = 314 100π π π/π π = 314 πβ/ππ‘ = 314/100π πβ/ππ‘ = 314/(100 Γ 3.14) πβ/ππ‘ = 314/314 πβ/ππ‘ = 1 Since depth is in meter & time is in hr So, π π/π π = 1 m/hr. So, A is the correct answer.