Campbell's Test: Maximizing Volume
Here, we have a Campbell's Cream of Chicken soup can. [br][br]The height of this can = 4 in.[br]This can has a circumference of 8.25 in. [br][br]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? [br][br]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. [br][br]Suppose we keep this surface area constant = 43.8325 in^2. [br]Does Campbell's provide the customer with the greatest amount of soup that can fit inside such a can with fixed total surface area? [br][br]Explain why or why not.
4.
Algebraically determine the value of the radius that maximizes the amount of soup in the can.