# Volume of a right circular cylinder inscribed in a sphere

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.

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...ius r where h is the height of the cylinder.

Now the volume of the cylinder VCy = π k2 h

Now we will determine the values of k and h in terms of the radius of the sphere r. See the figure. Label the central angle of this triangle as T.

From the figure,

Sin[ T ] = h/2r Cos [ T ] = k/r

Therefore the volume of the cylinder is,

Vcy = 2π ...