Pappus' Theorem (surface area)

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Homework Help Overview

The discussion revolves around applying Pappus' Theorem to determine the centroid of a semicircle defined by the equation x = sqrt(c^2 - y^2). Participants reference the surface area of a sphere and the relevant equation for surface area in their attempts to understand the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the meaning of the equation and its components, questioning whether to convert the semicircle equation into a different form. There are inquiries about the specific surface area being referenced and the implications of the variables in the equation.

Discussion Status

The discussion is ongoing, with participants expressing confusion and seeking clarification on the variables involved in the equation. Some guidance has been offered regarding the interpretation of the semicircle equation, but no consensus has been reached on how to proceed.

Contextual Notes

Participants note a lack of understanding regarding the surface area context and the definitions of the variables in the equation, indicating potential gaps in foundational knowledge that may affect their ability to solve the problem.

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Homework Statement


Use Pappus' Theorem for surface area and the fact that the surface area of a sphere of radius c is 4(pi)c^2 to find the centroid of the semicircle x= sqrt ( c^2 - y^2)


Homework Equations


S = 2 (pi) * p * L

where s=surface area; p=distance from axis of revolution; L= length of the arc


The Attempt at a Solution


1. centroid of semicircle. should i put the equation in circle form, and attempt to solve from that?
 
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whatlifeforme said:

Homework Statement


Use Pappus' Theorem for surface area and the fact that the surface area of a sphere of radius c is 4(pi)c^2 to find the centroid of the semicircle x= sqrt ( c^2 - y^2)

Homework Equations


S = 2 (pi) * p * L

where s=surface area; p=distance from axis of revolution; L= length of the arc

The Attempt at a Solution


1. centroid of semicircle. should i put the equation in circle form, and attempt to solve from that?

No, you don't. You need to think about what that equation means and how it's related to what you want to find. It's almost all you need to know.
 
i'm still lost.
 
whatlifeforme said:
i'm still lost.

Explain to me what the variables in that equation mean. Yes, S=surface area. But surface area of WHAT? Look it up if you don't have a good reference handy.
 
S = 2 (pi) * p * L

where s=surface area; p=distance from axis of revolution; L= length of the arc
 

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