# 18) Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle a is one-third that of the cone and the greatest volume of cylinder is

Let's take radius and height of cylinder = r and h ' respectively
Let's take radius and height of cone = R and h  respectively

Volume of cylinder =
Volume of cone =
Now, we have

Now, since  are similar

Now,

Now,

Now,

at

Hence,   is the point of maxima

Hence proved
Now, Volume (V) at  and     is

hence proved

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