anonymous
  • anonymous
Does anyone know any tips to follow for optimization problems and how to deal with the different shapes in them?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
whats the problem? we dont all see what you see :)
anonymous
  • anonymous
Find the height of the largest cylinder that can be placed inside a sphere whose radius is 4*the root of 3. I have the solution in front of me, but I don't understand how in a cylinder, the height will be divided into two, but in other shapes, a triangle inside a circle for example, that doesn't happen?
amistre64
  • amistre64
whose radius? cyl or sphere?

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More answers

anonymous
  • anonymous
sphere
amistre64
  • amistre64
we can take the cross section and just figure out the rectangle in a circle... right?
anonymous
  • anonymous
well, what they've done is create a mini triangle inside the cylinder, using the radius one of the triangles sides and having (h) height, and (x) being the other sides and then we do pythagorean theorem
amistre64
  • amistre64
like this right?
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amistre64
  • amistre64
do we want to maximize the area of the cyl? or just the height?
anonymous
  • anonymous
Like this: sorry for the cheesy sketch =P
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amistre64
  • amistre64
area...volume; same diff :)
amistre64
  • amistre64
its a good pic :) but without any restrictions to the cylindar; the max height can be close to the "diameter" of the sphere right? the question seens to be missing something
anonymous
  • anonymous
In another problem, where there's a triangle inside a sphere, the height doesn't get divided like that, instead they take the whole height, and the perpendicular side would become (h-(whatever radius they give). How do I deal with all these different shapes?
amistre64
  • amistre64
this is usually associated with the question: What is the largest volume right sylindar that can fit inside a sphere of radius (#)
amistre64
  • amistre64
the shapes I could deal with; its the missing information to make the question plausible thats getting me :)
anonymous
  • anonymous
yea, the solution in front of me seems pretty simple, but when i try to solve myself I always end up messing up somewhere...
amistre64
  • amistre64
What does: "Find the height of the largest cylinder" mean?? I assume its talking about volume....but i cant tell :) the height of the cylindar is only limited by the diameter of the sphere....whats the answer they give?
anonymous
  • anonymous
there is no missing info, from the sketch you get a constraint that's like this (r^2=48-h^2) and you use that for r^2 in your function which is the volume of the cylinder (V= pie*r^2h)
amistre64
  • amistre64
So it IS volume we want to maximize....right?
anonymous
  • anonymous
then you take the first derivative and let it equal zero, and solve for height. I guess I just thought there was a general rule that could be followed.
amistre64
  • amistre64
which of these is the radius of the sphere? \[\sqrt[4]{3} \leftarrow \rightarrow 4\sqrt{3}\]
anonymous
  • anonymous
second one
amistre64
  • amistre64
good :) then we can work this easier :)
anonymous
  • anonymous
the end reply for h=4 cm, since h was divided into two, the height would be 2h, therefore 8 cm =)
amistre64
  • amistre64
it pretty much boils down to this; what is the largest area rectangle you can fit under a quarter top circle..
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amistre64
  • amistre64
the equation of a circle is: x^2 + y^2 = r^2 y^2 = r^2 - x^2 y = sqrt(48 - x^2); where x is an interval from 0 to 4sqrt(3)
amistre64
  • amistre64
4sqrt(3) ------- = 2 sqrt(6); the height for max volume should be 4 sqrt(6) sqrt(2)
amistre64
  • amistre64
is that the right answer? :)
anonymous
  • anonymous
h=4 cm, height=2h, therefore, maximum height=8 cm
anonymous
  • anonymous
thank you! :)
amistre64
  • amistre64
if I was helpful; youre welcome :)

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