Sixteen meter of wire is available to fence off a flower bed in the form of a sector of a circle. If the flower bed has the maximum surface area, then the radius is

Let ‘r’ be the radius of the sector and angle subtended at the centre be θThen, S=Surface area of sector=θ360×πr2 We know θ= length of arc  radius =16−2rrS=θ2ππ⋅r2=16−2r2rr2S=(8−r)⋅r=8r−r2⇒dSdr=8−2rNow for area to be maximum⇒dSdr=0⇒r=4