Q. 245.0( 1 Vote )
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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