Q27 of 46 Page 1

Show that the right circular cylinder, open at the top, and of given surface area and maximum volume is such that its height is equal to the radius of the base.


The radius of cylinder = r


The height of cylinder = H


Now acc. to the question:


⇒


Now volume of cylinder =


⇒…(2)


For V to be maximum


⇒


⇒


⇒


⇒S=2πr …(3)


Differentiating again we get,



Which implies maximum value.


Put (3) in (1),


We get:


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