Posted by ali on Saturday, July 12, 2014 at 12:08am.
Show that a right-circular cylinder of greatest volume that can be inscribed in a right-circular cone that has a volume that is 4/9 the volume of the cone.
mathe - MathMate, Saturday, July 12, 2014 at 6:21am
Let the cone radius = R
cone height = H
Let cylinder height = h
then cylinder radius, r = R(1-h/H)
Volume of cylinder, V
For maximum volume,
which simplifies to:
which when solved for h gives
h=H/3 or h=H
h=H will give a zero volume (min.) so reject.
Volume of cylinder
=4/9 volume of the cone.
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