1. Module 2

1.13. Page 3

Mathematics 10-3 Module 2

Module 2: The Imperial System

 

Explore

 

When you double the dimensions of a rectangle, you increase the rectangle’s area not by a factor of 2, but by a factor of 4.

 

For example, if you have a mat measuring 2 ft × 3 ft, the mat’s area is 6 ft2. If you double its dimensions, it becomes a mat with the measurements of 4 ft × 6 ft. The area of this larger mat is 24 ft2. This larger mat has an area four times the smaller mat.

 

What happens to the volume of something when its dimensions are increased by a factor? You will investigate this question in the next activity.

 

m10_3_trythis.jpg Try This

 

In this activity you will investigate the effect increasing all three dimensions of your bedroom has on your bedroom’s volume.

 

You will need a ruler or tape measure that shows feet and inches and your estimation skills.

 

Do you remember the formula used to calculate the volume of a rectangular, prism-shaped object?

 

Work with a partner if possible.

 

This is a photo of house blueprints with a compass and pencil laying overtop.

iStockphoto/Thinkstock

Measure the length, width, and height of your bedroom. Round each dimension to the nearest foot.

 

TT 5. Record these dimensions and calculate the volume.

 

TT 6. How would you calculate the number of cubes (1 ft on each side) needed to fill your bedroom? How do you think the volume of air in your bedroom relates to the number of cubes? Explain your reasoning.

 

TT 7. Double each dimension of your bedroom. Record these new dimensions. Now calculate the volume of a room with these dimensions. How many times has the volume increased?

 

TT 8. Next, triple the dimensions of your bedroom. Calculate the volume of such a room. Compare this volume with the original volume of your room. Once again, how many times has the volume increased?

 

TT 9. What is the relationship between the new volumes and the number of times you increased the dimensions?

 

m10_3_share.jpg Share

 

It’s time to share your answers to TT 5–TT 9. Remember that sharing work is an important part of learning. Use the following tips to ensure you get all the benefits from this sharing opportunity.

  • Complete the questions to the best of your ability. Make sure your answers are in a form that you can easily share with another student or with your teacher, if so directed.
  • Use your class discussion area, or another method indicated by your teacher, to post your answers and to view the work of the people you’re sharing with.
  • Compare your answers to the other posted answers. Identify where you have similar answers and where your answers are different. Discuss all differences between answers until you agree on the answers. If necessary, you may wish to involve your teacher in your discussion.
  • Revise your answers where necessary.

Save a revised copy of your work in your course folder. Ask your teacher whether you should also save a summary of your discussion in your course folder.

 

V = l × w × h, where l is the length, w is the width, and h is the height.