Q. 274.0( 4 Votes )

Show what the max

Answer :


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







Therefore,





x = - 5 cannot be taken as the length cannot be negative.


At x = 5, we have to check whether maxima exits or not.


Therefore,



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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