Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius `5sqrt(3)c m` is `500pic m^3dot`

Explanation

Let h and r be the height and radius of the inscribed cylinder

In`△OAC,OC^2+CA^2=OA ^2`

⇒`( h/2​ )^2 +r ^2` =`(5 sqrt3​ )^ 2`

`∴r ^2 =75− h^2/4`

volume of the cylinder,

v=`πr ^2 h`

v=`π(75− h^2/4 )h`

∴v= `π/4​ (300−h^ 3 )`
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