Question

17. Show that the height of the cylinder of maximum volume that can be inscribed in
a sphere of radius R is 2R
3
. Also find the maximum volume.

Answer 1

Let R be the radius of the sphere

let h be the height

and x be the diameter of cylinder

in △Abc.

Using Pythagoras theorem

${(cb)}^{2} + {(ab)}^{2} = {(ac)}^{2}$

${h}^{2} + {(x)}^{2} = {(r + r)}^{2}$

${h}^{2} + {x}^{2} = {4r}^{2}$

${x}^{2} = {4r}^{2} - {h}^{2} \: - - - - eq.1$

We need to find maximum Volume of cylinder

let v be the volume of the cylinder

rest in the pic

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