Campbell's Test: Maximizing Volume
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 inchess of metal are used to make this can? (Hint: Find the surface area!)
3.
How many centimeters cubed of soup can the can hold? (Hint: Find the volume!)
After answering this question, please be sure to keep scrolling and answer the questions located below the GeoGebra applet (below).
4.
When you move the gray circle in the applet above, what stays the same?
5.
When you move the gray circle in the applet above, what two things change?
6.
Campbell's can make cans that use the same amount of metal (43.8325 square inches), but that have different volumes.
Is the volume of the actual can the highest possible volume given the surface area of 43.8 square inches?
Explain why or why not.
7.
Use the applet above to estimate the radius of the can with the highest possible volume given a surface area of 43.8 square inches.