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  • The radius of a right circular cylinder of maximum volume Which can be inscribed in a sphere of radius R is

The radius of a right circular cylinder of maximum volume Which can be inscribed in a sphere of radius R is

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Solution:  Let   r  be radius of cylinder

         R be radius of sphere

        Let  CM=x,V=pi(R^2-x^2)2x

     For  Maximum volume      fracmathrmd Vmathrmd x=0

 \ \ Rightarrow x=fracRsqrt3,r=sqrtR^2-x^2,r=sqrtR^2-fracR^23;

               r=sqrtfrac23R^2=sqrtfrac23R    and   verify   fracmathrmd ^2Vmathrmd x^2< 0

 

Posted by

Deependra Verma

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