Calculus Homework Help - Optimization Word Problem

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SUMMARY

The discussion centers on solving an optimization problem in calculus, specifically determining the height and radius of a cylinder with the greatest volume that can be inscribed in a sphere of radius R. The solution involves using derivatives to find the maximum volume. The participant initially struggled with visualization but ultimately resolved the problem independently, indicating that understanding the geometric relationship is crucial for solving similar problems.

PREREQUISITES
  • Understanding of calculus concepts, particularly derivatives
  • Familiarity with optimization problems in mathematics
  • Basic knowledge of geometric shapes, specifically cylinders and spheres
  • Ability to visualize geometric relationships in three dimensions
NEXT STEPS
  • Study optimization techniques in calculus, focusing on derivative applications
  • Explore problems involving volumes of solids, particularly cylinders and spheres
  • Learn about geometric visualization strategies to aid in solving complex problems
  • Practice additional optimization problems to reinforce understanding of concepts
USEFUL FOR

Students in calculus courses, educators teaching optimization techniques, and anyone seeking to improve their problem-solving skills in mathematics.

markcus
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Calculus Homework Help -- Optimization Word Problem

I'm in a University Calculus class, and I am having trouble with one of my homework questions. Much help would be appreciated!

"Determine the height and radius of the cylinder of greatest volume that can be inscribed in a sphere of radius R units."

Also, we are learning about derivatives, so if the question is solved using them, please indicate!
Thank you so much!.
 
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welcome to pf!

hi markcus! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 


hey i actually figured it out, i think i was just having trouble visualizing it, it's not that bad though. but thanks!
 

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