# Campbell's Test: Maximizing Volume

- Author:
- Tim Brzezinski

Here, we have a Campbell's Cream of Chicken soup can.
The height of this can = 4 in.
This can has a circumference of 8.25 in.
Please refer to the questions below the pictures.

## HEIGHT = 4 in

## CIRCUMFERENCE = 8.25 in

## 1.

What would the radius of this can be?

## 2.

How many square cm of metal is used to make this can? After answering this question, please be sure to answer the questions located below the GeoGebra applet (below).

## 3.

Interact with the GeoGebra applet above for a few minutes. If you drag the point on the right, you'll create various cylinders (on the left) with constant surface area = 43.8325 in^2. Suppose we keep this surface area constant = 43.8325 in^2. Does Campbell's provide the customer with the greatest amount of soup that can fit inside such a can with fixed total surface area? Explain why or why not.

## 4.

Algebraically determine the value of the radius that maximizes the amount of soup in the can.