Q17 of 168 Page 242

Show 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.

Let r and h be the radius and the height of the cylinder respectively.

Now, h =


The volume (V) of the cylinder is given by:


V = πr2h =2 πr2






Now, if



Now,




Now, we can see that at, , < 0.


Therefore, the volume is the maximum when.


When , the height of the cylinder is .


Therefore, the volume of the cylinder is the maximum when the height of the cylinder is .


Hence Proved.


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