question_answer

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower -bed, is :-       JEE Main Solved Paper-2017

A)  30                                         

B)  12.5

C)  10                                         

D)  25

Correct Answer: D

Solution :

 Total length \[=r+r+r\theta =20\]                                 \[\theta =\frac{20-2r}{r}\] \[Area=\frac{1}{2}{{r}^{2}}\theta =\frac{1}{2}{{r}^{2}}\left( \frac{20-2r}{r} \right)\] \[A=10r-{{r}^{2}}\] \[\frac{dA}{dr}=0\]         \[10-2r=0,\,r=5\] \[A=50-25=25\]