# Cylindrical Math Project

### Brian Karlow, Rebecca Mackenzie, Natalie Reed

This is our poster for the Linking Cans, Cylinders, and Rational Equations project. Below we have our steps to finding the solutions to both Part 1 and Part 2.

## PART 1

### Step A

We determined that the volume of a cylinder is V=(3.14)(r^2)(h)

Pi is used because the circumference and the diameter are both legs and they both need a ratio.

### Step B

In step B we had to draw a net diagram of an aluminum can:

Verbal Model: cost= 6 cents times 2 lids plus 4 cents times 1 can Mathematical Model: cost= 2[(.06)(3.14)(r^2)] + 2[(.04)(3.14)(r)(h)]

### Step C

In step C our group had to find an equation for the cost of the aluminum can. The picture below shows our work to find the equation and the final equation that we will eventually use to find the total cost of the can.

Step C also requires a list of all the specific requirements needed in the final equation: -The cost of the aluminum -Pi -Radius

### Step D

In the final step of Part 1 it asks us to find the final cost of the can, what the dimensions of the can are, and how we found both of these things.

Below is our work for finding both the total cost of the can and the dimensions of the can as well. Our group found the dimensions of the can by plugging 2.4 into the volume equation and then solving for h. We found the minimum cost by substituting 2.4 in for r. We plugged the equation into our calculator and the output is the final cost of the can.

## PART 2

Part 2 of our project lets us choose our own aluminum can, with that can we will need to find the dimensions of the can and the total cost of the aluminum.

We chose a can of black beans, that has a 1.06 inch radius and a 4.3 inch height. Which means that the can should be approximately 355 mL.

To find the surface area (SA) of the can we used the same equation that we used in Part 1. The picture below shows all of our steps to find the new equation for the new cost of the can.

2. There are differences between our model and the actual product. This means that our cost for the production of this can at the given specifications may not be exactly what it costs to manufacture the can. The reason for this is that it costed .60 cents for the lid and bottom of the can and .40 cents for the sides. In real life this may not be the actual cost needed to make one can so, there will be a difference in the cost value model. This change would be shown in the values of the sides, top, and bottom of the can. .60 and .40 would be replaced with the actual cost.

For Part 2 we used a can of black beans to for our dimensions.

I got this picture from www.bonappetit.com/

This video is a song that talks about how to find the volume of a cylinder. It directly relates to our project because it explains the formula used to find the volume of a cylinder. Video Credit to Joe Reid via YouTube.