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# Linking Cans, Cylinders, and Rational Equations

By: Alexis Nakoneczny, Cassidy Bowers, Melake Abebaw

## Part i

The volume of a cylinder is V=πr^2h. πr^2 is the area of a circle, (one of the basic shapes found in a cylinder.) In order to find the volume, you must multiply the area of a cylinder by the height of the cylinder.

As seen in the picture, the total cost equation incorporates the area of the 2 circles that make the top of the bottom and the rectangle that makes up the sides. It also includes the cost of the top/bottom and the cost of the sides.

## Part ii

This was the cylinder that my group used for part II

After measuring our cylinder, we found that the radius was .84 in and the height was 7.69 in.

We plugged the dimensions into the equation we created in part 1 question b, but we changed the .4 and .6 to .2 and .3. We simplified the equation and found the cost of the bottle to be \$9.45 when the top material costs 3 cents and the sides cost 2 cents. Essentially, at these costs, it will take \$9.45 to produce each Bath and Body Works perfume bottle. At this rate, the perfume inside the bottle costs \$4.55 (The price is \$14).