The maximum volume cylinder will be carved when the diameter of sphere and the axis of cylinder coincide.
Let h be the height of our cylinder.
r be the radius of the cylinder.
R = 53 radius of the sphere
OL = x
H = 2x
In Δ AOL,
Volume of cylinder V = πr2h
x = - 5 cannot be taken as the length cannot be negative.
At x = 5, we have to check whether maxima exits or not.
At x = 5, is negative. Hence, maxima exits at x = 5.
Therefore, at x = 5
Volume of Cylinder = π(75 - x2)(2x)
Volume = π(75 - 25)(10) = 500π
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