Max Area of Frustrum: Parabola & Line Constraint

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Homework Help Overview

The discussion revolves around finding the maximum area of a frustrum bounded by a parabolic curve defined by the equation y = -x² + 16 and the line y = 0. The problem involves concepts from calculus and geometry.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the maximum area of the frustrum, with one individual questioning a potential solution based on a quick mental calculation. Another participant expresses a desire for clarification on the reasoning behind the calculation, indicating a personal connection to the problem.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and seeking clarification. There is an emphasis on the need for showing work and reasoning, rather than providing direct solutions. Some participants are reflecting on their understanding and experiences related to the problem.

Contextual Notes

One participant mentions the ratio of radius and height of the small and big cone, indicating a potential geometric relationship that may be relevant to the problem. There is also a note about the forum's policy against providing direct solutions to homework problems.

mathwiz123
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Find the maximum area of a frustrum bounded by a paroloid and line y=0. (constraining parabola =-x^2 + 16.)
 
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Is it 4*64/3? (Quick mental calculation).
 
Can you show how you did it? Cause this is something I've thought about after my son showed me his math homework a few years back. Found this forum, and decided to see if you guys knew.
 
Sorry, we don't provide the solutions to homework problems here. If you show your work and explain your reasoning, we can help you when you get stuck. BTW, the "my son showed me this a few years back and I can't stop thinking about it" line is unnecessary -- you aren't going to trick us into doing your homework for you.

- Warren
 
I was actually serious...I understand that you find a lot of kids on the site. I thought of this problem today when trying to build a brace for a parabaloid shaped piece. I thought of a lot of different shapes to put in it. Cylinder, cone, etc. Frustrum came to mind and I thought of the homework problem. I'm sure I could consult any calculus textbook, but you folks seemed to provide interesting responses. If you want my "work" I know the ratio of radius and height of the "small" and "big" cone are equal. But that's all I know.
 

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