Question

Calculus - Optimization Problem: A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 3. What are the dimensions of such a cylinder which has maximum height?

Radius = __?__ and Height = __?__

Answer 1

Is there some info missing. A cylinder of max height would be 5.5 . there must be some other constraint like maximize the vol of the cylinder, etc

Answer 2

I wish it had more info, but that is all that was given to me.

Answer 3

which has maximum height? or maximum volume?

Answer 4

If the question asks for maximum volume, then create the constraint for the cylinder.
h/2 + r = 3 (h=0, r=3, h=6, r=0)

The volume function is then
V=pi r^2h = pi(r^2) 2(3-r)
and
dV/dr = 6pi r(2-r) = 0 for max or min.
r=0 for min, and
r=2 for maximum volume.

Guess you can take care of the rest.