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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    Twenty two metres are available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, the radius of the circle must be:

    A)  4m                                        

    B)  3 m

    C)  6m                        

    D)         7m

    E)  5m

    Correct Answer: E

    Solution :

    \[\because \]     \[l=\frac{2\pi r\theta }{360{}^\circ }\] \[\Rightarrow \]               \[22=r+r+\frac{2\pi r\theta }{360{}^\circ }\] \[\Rightarrow \]               \[\theta =\left( \frac{22-2r}{2\pi r} \right)360{}^\circ \] Now,     \[A=\frac{\pi {{r}^{2}}\theta }{360{}^\circ }=r(11-r)\]                 \[\frac{dA}{dr}=11-2r\]and\[\frac{{{d}^{2}}A}{d{{r}^{2}}}=-2\]                 \[{{\left( \frac{{{d}^{2}}A}{d{{r}^{2}}} \right)}_{r=\frac{11}{2}}}=-2<0\]   \[\therefore \]Area is maximum when\[r=\frac{11}{2}\]. \[\therefore \]Possible radius of circle must be 5 m.


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