# Math - Optomization

A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 5.5. What are the dimensions of such a cylinder which has maximum volume?

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1. in the cylinder, upside down.

diameter=5.5(6.5-h)/6.5

volume=PI*h*D^2/4

V=PI/4*h*(5.5/6.5)^2*(6.5-h)
V=PI/4*(5.5/6.5)^2 (6.5h-h^2)
dV/dh=0=6.5-2h
h=3.25
d=5.5/6.5(3.25)=5.5/2=2.75

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