Volume and surface area of a cylinder

AI Thread Summary
To find the ratio of the volume to the surface area of a cylinder, the volume is calculated as V = πr²h and the surface area as A = 2πr(h + r). The discussion emphasizes the need to compute the ratio V/A, which simplifies to (d²πh)/[(2πdh) + (2πd²)], where d represents the diameter. Participants clarify that d is not the radius and suggest further simplification of the ratio. The conversation focuses on correctly identifying the dimensions and applying the formulas to achieve the desired result.
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.
 
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You have expressions for the area and volume, you are told to compute the ratio

\frac {Volume} {Area}

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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