Be a Part of America’s Student Support Network
TutorMentorServe

Close

# Measurement Relationships

## Examine the relationships between area and perimeter when one measure is fixed. Determine which shapes maximize area while minimizing perimeter, and vice versa. Explore the proportional relationship between surface area and volume. Construct open-box containers, and use graphs to approximate the dimensions of the resulting rectangular prism that holds the maximum volume.

View Transcript

In This Session

Part A: Area and Perimeter
Part B: Surface Area and Volume
Part C: Designing a Water Tank
Homework

In this session, you will explore the dynamic relationships that exist among measurements, such as area and perimeter or surface area and volume. More specifically, you will look at what happens to one variable when the other one is fixed. You will also consider some practical applications of these relationships.

For information on required and/or optional materials, see Note 1.

### Learning Objectives

In this session, you will do the following:•Examine the relationships between area and perimeter when one measure is fixed•Explore which shapes simultaneously maximize area and minimize perimeter, and vice versa•Learn about the proportional relationship between surface area and volume and some of its applications•Construct open boxes and use graphs to approximate the dimensions of a rectangular prism that holds the maximum volume

### Key Terms

Previously Introduced:

Area: Area is a measure of how much surface is covered by a figure.

Perimeter: Perimeter is the length or distance around a closed curve or a shape.

Surface area: Surface area is the area enclosing a three-dimensional or solid object. You can find it by taking the sum of the areas of all of the surfaces of a three-dimensional object.

Volume: Volume is the three-dimensional space taken up by an object.

### Notes

Materials Needed

• Scissors
• Tape
• Graphing calculator (optional)
• Multilink cubes (3/4 in. cubic units that snap together)
• Square one-inch tiles (optional)