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QJEEM19Ma8dad: JEE Main 2019 Mathematics - Class 12 JEEM19Ma8dad Solution: A spherical iron ball of radius 10 cm is coated with a layer of …

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3 /min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

Multiple Choice Options

  • A 56π{5 \over {6\pi }}
  • B 19π{1 \over {9\pi }}
  • C 136π{1 \over {36\pi }}
  • D 118π{1 \over {18\pi }}

Step-by-Step Verified Solution

JEE Main 2019 (Online) 10th April Evening Slot Mathematics - Application of Derivatives Question 146 English Explanation
V=43π((10+h)3−103)V = {4 \over 3}\pi \left( {{{\left( {10 + h} \right)}^3} - {{10}^3}} \right)

⇒dVdt=4π(10+h)2dhdt\Rightarrow {{dV} \over {dt}} = 4\pi {(10 + h)^2}{{dh} \over {dt}}

⇒−50=4π(10+5)2dhdt\Rightarrow - 50 = 4\pi {\left( {10 + 5} \right)^2}{{dh} \over {dt}}

⇒dhdt=−118π\Rightarrow {{dh} \over {dt}} = - {1 \over {18\pi }}

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