2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in \[\text{c}{{\text{m}}^{\text{2}}}\]/hour) is.   JEE Main Online Paper (Held On 26-May-2012)  

    A) \[5\pi \]               

    B)                                        \[10\pi \]

    C)                        \[100\pi \]                          

    D)                        \[50\pi \]

    Correct Answer: B

    Solution :

    Let \[A=\pi {{r}^{2}}\] be area of metalic circular plate of \[r=50\] cm. Also, given\[\frac{dr}{dt}=1mm=\frac{1}{10}cm\] \[\therefore \]\[A=\pi {{r}^{2}}\] \[\Rightarrow \]\[\frac{dA}{dt}=2\pi r\frac{dr}{dt}=2\pi .50.\frac{1}{10}=10\pi \] Hence, area of plate increases in\[10\pi c{{m}^{2}}/\]hour.


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