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Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radiusRis. Also find the maximum volume.

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A sphere of fixed radius (R) is given. Let r and h be the radius and the height of the cylinder respectively. From the given figure, we have The volume (V) of the cylinder is given by, Now, it can be observed that at. ∴The volume is the maximum when When, the height of the cylinder is Hence,...
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A sphere of fixed radius (R) is given. Let r and h be the radius and the height of the cylinder respectively. From the given figure, we have The volume (V) of the cylinder is given by, Now, it can be observed that at. ∴The volume is the maximum when When, the height of the cylinder is Hence, the volume of the cylinder is the maximum when the height of the cylinder is. read less
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