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 flowerbed is

Step-by-step solution

Total length of wire =r+r+r aligned & 20=2 r + r & = 20-2 r r aligned aligned & A= 1 2 r^2 & = 1 2 r^2 ( 20-2 r r )=10 r-r^2 & d A d r =10-2 r aligned For maximum area, dA dr =0 aligned & 10-2 r =0 & r =5 & ~d ^2 ~A dr ^2 =-2 0 aligned Area is maximum at r =5 aligned Maximum area & =10(5)-5^2 & =50-25=25 sq . m aligned