2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Afternoon)

  • question_answer
    A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of \[50\text{ }c{{m}^{3}}/min.\]When the thickness of the ice is 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is : [JEE Main 10-4-2019 Afternoon]

    A) \[\frac{1}{9\pi }\]                   

    B)   \[\frac{5}{6\pi }\]

    C) \[\frac{1}{18\pi }\]     

    D) \[\frac{1}{36\pi }\]

    Correct Answer: C

    Solution :

    \[V=\frac{4}{3}\pi \left( {{(10+h)}^{3}}-{{10}^{3}} \right)\]           \[\frac{dV}{dt}=4\pi {{\left( 10+h \right)}^{2}}\frac{dh}{dt}\]           \[-50=4\pi {{\left( 10+5 \right)}^{2}}\frac{dh}{dt}\]           \[\Rightarrow \]\[\frac{dh}{dt}=-\frac{1}{18}\frac{cm}{\min }\]                 


You need to login to perform this action.
You will be redirected in 3 sec spinner