Volume and surface area of a cylinder

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Homework Help Overview

The discussion revolves around finding the ratio of the volume to the surface area of a cylinder, with a specific focus on expressing this ratio as a function of diameter (D). Participants are examining the relevant formulas for volume and surface area in the context of this problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the expressions for volume and surface area, with some attempting to derive the ratio of volume to area. Questions arise regarding the correct interpretation of the variables involved, particularly the distinction between diameter and radius.

Discussion Status

The conversation is progressing with participants providing initial calculations and suggestions for simplification. There is an acknowledgment of potential confusion regarding the definitions of the variables, indicating a productive exploration of the problem.

Contextual Notes

There is a mention of an image reference that may provide additional context, though it is not accessible within the discussion. Participants are also navigating the implications of using diameter instead of radius in their calculations.

Paulo Serrano
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Homework Statement


I need the ratio like in the image below
http://img228.imageshack.us/img228/4015/foiessa.jpg
I guess as a function of D.

Homework Equations


Volume of a cylinder: pi*r^2*h
Area: 2*pi*r*(h+r)

The Attempt at a Solution



No clue.
 
Last edited by a moderator:
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You have expressions for the area and volume, you are told to compute the ratio

[tex]\frac {Volume} {Area}[/tex]

What is your problem?
 
The area of a cylinder, as far as I remember, is: 2*pi*r*h +(2*pi*r^2)
 
Now find the the volume, and divide that by area.

V= d^2*pi*h

A= (2*pi*d*h) + (2pi*d^2)

And now write V/A = (d^2*pi*h)/[(2*pi*d*h) + (2pi*d^2)]

I hope I am right, and that it helps! :)
 
That is a good start. Now do some simplification.
 
d isn't the radius though.
 

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