1. Lesson 7: Optimizing Areas and Volumes of Rectangular Prisms
LG: I can determine the maximum area.
I can determine the minimum perimeter.

2. Maximum Volume
Among all rectangular prisms with a given surface area, a cube has the maximum volume.
Example 1
John constructs a rectangular prism using exactly 384 square inches of cardboard. It has the greatest possible volume. What are the dimensions of the prism? What is its volume?

3. Minimum Perimeter
Among all rectangles with a given volume, a cube has the minimum surface area.
Example 2
Rosie constructs a rectangular prism with a volume of exactly 1331 m3. It has the least surface area possible. What are the dimensions of the prism? What is its surface area.

4. Maximize volume with constraints
Yael is designing a glass candle holder. It will be a rectangular prism with outer surface area 225 cm2, a square base, and no top.
a) Determine the maximum volume of the candle holder.
b) What are the dimensions of the candle holder with the maximum volume?

5. Practice Questions
Page 110 #1-4, 6, 10 and 9.