Q. 24 5.0( 1 Vote )

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

Answer :

The perimeter of the rectangle with length L and breadth b is 2(l + b)


2(L + b) = 36

L + b = 18

b = 18 - L

Let the rectangle be rotated about its breadth. Then the resulting cylinder formed will be of radius L and height b.

Volume of cylinder formed V = πL2b = π(18L2 - L3)

To find the dimensions that will result in the maximum volume:

L cannot be 0. L is taken as 12 cm.

Therefore b = 24.

At L = 12,

Therefore a maxima exists at L = 12, meaning the volume of the constructed cylinder will be maximum at L = 12 cm.

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