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The Optimal Surface area to Volume Ratio for Wine Barrels
Note this section involves some basic math... Lets determine the ratio of surface area to volume for several sized oak wine barrels. For simplicity, lets assume that a wine barrel is a cylinder. (In reality, a wine barrel has some curvature along the length. To analyze this correctly, we would need to use calculus, but that would unnecessarily complicate our analysis.)
From our high school geometry class, we know that the volume of a cylinder is expressed as:
Volume = PI * Radius * Radius * Height
Now, we should also recall that the area of a cylinder is expressed as:
Area = 2* PI * Radius* Height
Now, taking the area to volume ratio of our wine barrel we get:
Area / Volume = 2 * PI * Radius * Height / PI * Radius * Radius * Height
Canceling terms, this yields the simple expression:
Area / Volume = 2 / Radius
So the surface area to volume relationship is simply two divided by the radius of our wine barrel.
Now, lets compare this relationship for various size wine barrels:
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