Finding the Area or the Circumference of a gutter.

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Homework Help Overview

The discussion revolves around a mathematics assignment related to finding the area or circumference of a gutter, specifically focusing on the implications of these measurements in the context of material costs.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between area and circumference, questioning whether to focus on one or both for the assignment. There are discussions about minimizing perimeter for a fixed area and the variability of area with constant perimeter.

Discussion Status

The conversation is active, with participants raising questions about the implications of their findings and exploring different interpretations of the problem. Some guidance has been offered regarding the relationship between perimeter and area, but no consensus has been reached.

Contextual Notes

Participants are considering the practical application of their findings in relation to material costs and are grappling with the definitions and relationships between area and perimeter in their calculations.

Liparulo
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Hey Guys,
For a maths assignment, we were given this question to complete:
http://nrich.maths.org/5673

I'm having an discussion with a friend of how best to approach it. Should I work out and differentiate the area or perimeter (for the circle)? If we're finding the cost of materials, then circumference would be more appropriate than the area. Or should we look at both?
Sigh, isn't it always the most basic part of a problem that stumps us?
Thanks for your assistance.
 
Last edited:
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You want to minimize the perimeter (or circumference) for a fixed area.
 
The same perimeter can have a varying area, correct? Or would it be the same area every time? For example, if I curve a piece of paper, I can make the shape wider or smaller, but the perimeter stays the same. Is the area changing even though perimeter stays constant? Thanks.
 
Liparulo said:
The same perimeter can have a varying area, correct?

Yes. For any given perimeter p, you can range from the minimum area of 0 - by having a rectangle with length p/2 etc. - to the maximum area of...
 
So, (sorry to continue asking questions, but this is helping), would I find the perimeter of the circumference minus the perimeter of the arc? What role does area play in determining an equation?
 

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