How to Maximize the Volume of a Buoy Made from Two Equal Circular Bases?

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SUMMARY

The discussion focuses on maximizing the volume of a buoy constructed from two equal circular bases, specifically cones with a common base radius. The optimal radius for the base of the buoy is determined to be r = (sqrt(6) * R) / 3, where R represents the radius of the original circular bases. Participants clarify the concept of a buoy and its purpose as a water marker, while seeking further understanding of the geometric problem presented.

PREREQUISITES
  • Understanding of geometric shapes, specifically cones
  • Knowledge of volume calculation for three-dimensional objects
  • Familiarity with optimization techniques in mathematics
  • Basic algebra for manipulating equations
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  • Study the principles of volume optimization in geometric shapes
  • Learn about the properties and formulas related to cones
  • Explore mathematical techniques for solving optimization problems
  • Review examples of real-world applications of buoy design and construction
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Mathematicians, engineering students, and anyone interested in geometric optimization and buoy design will benefit from this discussion.

leprofece
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From two places equal of radio circular R It wants to build a buoy consists of two equal bass common cones

Determine the radius of Ia base when the volume of the buoy is maximum.

r=(sqrt of 6) R/3
 
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Re: Max and min

I must confess I have little idea what you are asking. I am assuming a buoy is to be constructed by joining two cones at their bases, but other than that I have no idea what is going on.
 
Re: Max and min

MarkFL said:
I must confess I have little idea what you are asking. I am assuming a buoy is to be constructed by joining two cones at their bases, but other than that I have no idea what is going on.

well, what you said is the main idea
a buoy is something put ond the water on beaches as a limit so that people can not go further if they do not do that they can die
 
Re: Max and min

leprofece said:
well, what you said is the main idea
a buoy is something put ond the water on beaches as a limit so that people can not go further if they do not do that they can die

Yes, I understand that a buoy is used as a marker on the water, but it is the problem I don't understand. Can you provide a diagram?
 
Re: Max and min

from two pieces that are the same i mean equal of radius R , from these i want to built the buoy
there is no graph in my book
ahhh. the pieces are circular both
 

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