# Application Of Derivatives

#### Question 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 *α*
is one-third that of the cone and the greatest volume of cylinder
istan^{2}*α*.

#### Answer:

The given
right circular cone of fixed height (*h)* and semi-vertical
angle (*α**)* can
be drawn as:

Here, a
cylinder of radius *R* and height *H* is inscribed in the
cone.

Then, ∠GAO
= *α*, OG =* r*,
OA = *h*, OE = *R*, and...

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