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

Therefore,

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.