Question

# Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle between the bounding radii) is

Solution

## The correct option is C Perimeter=2r+rθ=k (const.)Area=θ2r2=12(k−2r)rA=12(kr−2r2)dAdr=12(k−4r)=0⇒r=k4 d2Adr2 < 0 Now,2r+rθ=kk2+kθ4=kθ=2

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