Show that height of the cylinder of greatest volume which can be inscribed in a right…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

15. 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

\alpha

is one-third that of the cone and the greatest volume of cylinder is

\frac{4}{27} \pi h^{3} \tan ^{2} \alpha