Find the dimensions of the rectangle of perimeter 36 cm whi…

Maths Differentiation and Applications of Derivatives Maxima and Minima Subjective Type

Published on: August 14, 2026

Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible when revolved around one of its side .

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CHECK THE SOLUTION.

Let x, y be dimensions of rectangle.

⇒ 2x + 2y = 36.

Let V be volume sweeped

V = π x 2 y

V = π x 2 (18 – x)

= π x.3.(12 – x)

At x = 12, V has maximum value.

⇒ y = 6

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