Q.

The height of the cylinder of maximum volume that can be inscribed in a sphere of radius ‘a’ is

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a

a3

b

5a3

c

7a3

d

2a3

answer is D.

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Detailed Solution

Let h be the height and r be the radius of the cylinder. Let O be the centre of the sphere from diagramOA2=OP2+PA2a2=h24+r2...........1V=πr2h=πh.a2−h24V=πa2h−π4h3dvdh=πa2−π43h2d2vdh2=0−3π42h<0V is either max or mindvdh=0⇒h=2a3
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