## Saturday, April 26, 2014

### Coke Can Math Problem 3: Aluminum Coke Can Values

Aluminum Coke Can Values

Question One:  On April 17, 2014 the price of aluminum was \$0.83 per pound?  Recall from a previous blog that a regular empty Coke Can weighs 14 grams.  What is the value of the aluminum in a single Coke can?

There are 453.6 grams in a pound.

The value of the 14 gram can is (14/453.6) x \$0.83 or 0.0256.

Question Two:  What is the value of a Coke can that is filled with solid aluminum?  (Remember the radius of the can is 3.2 centimeters and the height of the can is 12.2 centimeters.)

First, the volume of the can must be obtained from the formula for the volume of the cylinder.  Intuitively this should be the area of the circle around the can multiplied by the height of the can.

V= H x pi x r2

V=12.2 x 3.142 x 3.22 = 392.6 cm3

Multiply by the density 2.8 gm/cm3 to get the mass.

Mass = 2.8 gm/cm3 x 392.5 cm3  =  1099.1 grams

From the first question above we know that the price of aluminum per gram is 0.0256/14 or 0.001829 \$.

Multiply price per gram \$0.001829 by 1099.1 grams to get our answer of \$2.0.

See summary of work in question two below:

 A solid aluminum can Height (cm) 12.2 pi 3.142 r (cm) 3.2 V (cm3) 392.5 Density (g/cm3) 2.8 Mass (gm) 1099.1 Price per gram (\$/gram) 0.001829 Value (\$) 2.0