# 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

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).