1. Optimal Surface Area & Volume
Square-Based Prisms
Cylinders

2. Note: Why do we want to minimize the surface area?
To save money (costs less for packaging)
To maximize the volume for a given surface area of a square-based prism, it is always a cube.
To minimize the surface area for a given volume of a square-based prism, it is always a cube.

3. Example #1
Determine the dimensions of a square-based prism with a maximum volume, given the surface area of 864 m2.
Calculate the volume.

4. Example #2
Tyler needs to construct a box to hold 6000cm3. What should the dimensions of the box be to minimize the amount of cardboard?
Calculate the surface area of the box.

5. Note:
The maximum volume for a given surface area of a cylinder will occur when the height and the diameter are equal.
The minimum surface area for a given volume of a cylinder will occur when the height and the diameter are equal.

6. Example # 1
A fertilizer company wants to make a cylindrical storage container out of metal. There is 30m2 of material available. What are the dimensions of the container that would maximize the amount of fertilizer that can be stored?
How much fertilizer could be stored?

7. Example #2
Baskin Robbins needs to design a cylindrical storage container that holds 1500cm3 of ice cream. What are the dimensions to minimize the amount of material needed?
What is the amount of material needed?

8. Homework
Pg. 480 # 1, 2, 5, 6, 11