The perimeter of a sector is p. The area of the sector is m…

Maths Differentiation and Applications of Derivatives Maxima and Minima Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The perimeter of a sector is p. The area of the sector is maximum when its radius is

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The correct answer is:

Perimeter of a sector = p . Let AOB be the sector with radius r. If angle of the sector be θ θ radians, then area of sector …..(i)

Length of arc( s ) = r θ θ or .

Therefore perimeter of the sector

…..(ii)

Substituting in (i), A =

⇒ ⇒ . Now substituting the value of s in (ii), we get or Differentiating with respect to we get . We know that for the maximum value of area or or .

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