Q. 29 5.0( 1 Vote )

Prove that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is Also find the maximum volume.

Answer :

The radius of cylinder = r

The radius of sphere = R

The height of cylinder = H

Now acc. to the diagram:

r = R cosθ …(1)


Now volume of cylinder =

For V to be maximum



Put (4) in (2),

We get:


Maximum Volume of cylinder = πr2 H

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