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# Surface Area of Cylinders

## SA = 2πr(h+r)

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Coca-Cola and Cylinder Surface Area

### Coca-Cola Cans

Recall that surface area is the total of the areas of each face on a solid figure. Also remember that the definition of a prism is a three–dimensional figure with two parallel congruent polygons as bases, with rectangular side faces. Finally, remember the formula for finding the surface area of a cylinder is \begin{align*}SA = 2 \pi r^2 + 2 \pi r h\end{align*}

Credit: User: Infrogmation
Source: http://commons.wikimedia.org/wiki/File:CocaColaBldgDavisPkwyNOLA.jpg

Coca-Cola plant in Davis [Figure1]

Coca-Cola facilities produce over 100,000 cans of Coke every day. Each can is sanitized several times, then filled with the proper ingredients, and finally is carbonated and sent to shipping. Coca-Cola is one of the most recognizable drinks in the world, and also makes for a great example for the surface area of cylinders.

#### Creative Applications

1. Research the average Coca-Cola can. What are it’s dimensions? According to this, what is the surface area a can of Coke?

Credit: User: Cane cane
Source: http://commons.wikimedia.org/wiki/File:Lata_Coca_Cola.JPG

How large is it? [Figure2]

2. Coca-Cola cans begin as plain aluminum cans. How much paint do they need to spray on the can to create the red and white logo? Why is this different from the surface area?

3. How would you find the surface area of other types of Coca-Cola cans?

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