Canned Soup : Maximizing Volume
[size=150]Here, we have a Cream of Chicken soup can. [br][br]The height of this can = 10 cm.[br]This can has a circumference of 20.5 cm. [br][br]Please refer to the questions below the pictures. [/size]
HEIGHT = 10 cm
CIRCUMFERENCE = 20. 5 cm
1.
[size=150]What would the radius of this can be? [/size]
2.
[size=150]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). [/size]
3.
[size=150]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 = 271.88 square cm [br][br]Suppose we keep this surface area constant = 271.88 square cm [br]Does the company making the soup can 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. [/size]
4.
[size=150]Algebraically determine the value of the radius that maximizes the amount of soup in the can. [/size]