1. CONFIDENTIAL 1 Grade 8 Changing Dimensions

2. Building a Bigger Box: Doubling the Volume of a Rectangular Prism. CONFIDENTIAL 2 1 2 3 1-2-3 box 2-4-6 box Volume = 1 x 2 x 3 = 6 units 3 Volume = 2 x 4 x 6 = 48 units 3 Volume has increased 8 times by doubling the dimensions! 2 4 6

3. Building a Bigger Box: Doubling the Volume of a Rectangular Prism. We need boxes with volume = 12 units 3 CONFIDENTIAL 3 1 2 3 1-2-3 box 1-2-6 box Volume = 1 x 2 x 3 = 6 units 3 Volume = 1 x 2 x 6 = 12 units 3 Volume has doubled! 1 2 6

4. Scaling Up the Compost Box: Applying Scale Factors to Rectangular Prisms The scale factor is the number that each dimension of one rectangular prism must be multiplied by to get the dimensions of a similar prism. The scale factor from the 1-2-3 box to the 2-4-6 box is 2 because each edge length of the 1- 2-3 box must be multiplied by 2 to get the corresponding edge length of the 2-4-6 box. CONFIDENTIAL 4 Remember: compost boxes are open on top!

5. Scaling Up the Compost Box: Applying Scale Factors to Rectangular Prisms What is the relationship between the corresponding dimensions of the two boxes? The larger box’s dimensions are twice those of the smaller box. What is the relationship between the surface areas of the two boxes? (The surface area of the larger box is 4 times that of the smaller box.) What is the relationship between the volumes of the two boxes? (The volume of the larger box is 8 times the volume of the smaller box.) What is the scale factor from the 1-2-3 to the 2-4-6 box? (The scale factor is 2.) So, are these two boxes similar? (These two boxes are similar because each dimension is multiplied by the same factor: 2.) CONFIDENTIAL 5

6. Building Model Ships: Similarity and Scale Factors Builders and architects often make models of cars, ships, buildings, and parks. A model is useful in determining several aspects of the building process, including structural strength, expense, and appearance. CONFIDENTIAL 6

7. Building Model Ships: Example: Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. If the length of the model is 25 centimeters, what is the length of the actual ship? 25 x 200 = 5,000 centimeters or 50 meters CONFIDENTIAL 7

8. Let us do some practice problems!

9. CONFIDENTIAL 9 1) A closed rectangular box has a height of 2 feet, a length of 4 feet, and a width of 4 feet. What is the volume of the box? a)32 ft 3 b)38 ft 3 c)36 ft 3 d)None of the above.

10. CONFIDENTIAL 10 2) What happens to the volume of a rectangular box if its dimensions are doubled? a)The volume will be 4 times as great b)The volume will be 6 times as great c)The volume will be 8 times as great d)The volume will be 10 times as great

11. CONFIDENTIAL 11 a)14 b)12 c)16 d)None of the above. 3) What are the dimensions of a box that is similar to a 1-2-3 box but has a volume of 10,368 cubic feet? What is the scale factor from the 1-2-3 box to the new box?

12. CONFIDENTIAL 12 4) Sandra wants to build a compost box that will decompose 8 times garbage than the amount of the 1-2-3 box. What are the dimensions of the new box? a)6-4-6 b)2-2-6 c)8-4-2 d)2-4-6

13. CONFIDENTIAL 13 5) When a ball is immersed in water, it displaces 36π cubic centimeters of water. What is the radius of the ball? a)2cm b)3 cm c)4 cm d)5 cm

14. CONFIDENTIAL 14 6) What are the dimensions of a box similar to a 1-2-3 box if the scale factor is 9? a)10-25-36 b)10-9-15 c)10-18-24 d)9-18-27

15. CONFIDENTIAL 15 7) What is the surface area of a compost box similar to a 1-2-3 box if the scale factor is 9? a)1,382 square unit b)1,296 square unit c)1,282 square unit d)1,482 square unit

16. CONFIDENTIAL 16 8) What is the volume of a compost box similar to a 1-2-3 box if the scale factor is 9? a)4,354 cubic units b)4,074 cubic units c)4,370 cubic units d)4,374 cubic units

17. CONFIDENTIAL 17 9) What are the dimensions of a compost box that is similar to a 1-2-3 box but has a surface area of 1600 square feet? a)10-25-35 b)20-20-36 c)10-20-30 d)10-50-40

18. CONFIDENTIAL 18 10) What is the scale factor of a compost box that is similar to a 1-2-3 box but has a surface area of 1600 square feet? a)16. b)9. c)20. d)10.

19. Assessment

20. CONFIDENTIAL 20 1) If you tripled each dimension of a 1-2-3 box, what would happen to the volume? a)It would be 27 times the original b)It would be 4 times the original c)It would be 8 times the original d)It would be 25 times the original

21. CONFIDENTIAL 21 2) What happens to the surface area if the dimensions are quadrupled? a)The surface area will be 14 times as great. b)The surface area will be 16 times as great. c)The surface area will be 9 times as great. d)The surface area will be 4 times as great.

22. CONFIDENTIAL 22 3) If the scale factor from a 1-2-3 box to a larger box is 4, how many 1-2-3 boxes will fit in the large box? a)66 b)75 c)64 d)77

23. CONFIDENTIAL 23 4) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. If the length of the model is 25 centimeters, what is the length of the actual ship? a)50 m b)25 m c)36 m d)40 in

24. CONFIDENTIAL 24 5) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. If the length of the flagpole on the actual ship is 30 meters, what is the length of the flagpole on the model? a)12 cm b)14 cm c)16 cm d)15 cm

25. CONFIDENTIAL 25 6) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. The area of a rectangular floor on the model is 20 square centimeters. What is the area of the floor on the actual ship? a)40 square meter b)60 square meter c)80 square meter d)100 square meter

26. CONFIDENTIAL 26 7) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. The cylindrical smoke stack on the model has a height of 4 centimeters and a radius of 1.5 centimeters. What are the dimensions of the smoke stack on the actual ship? a)radius = 3m; height = 8m b)radius = 3m; height = 6m c)radius = 2m; height = 8m d)radius = 4m; height = 10m

27. CONFIDENTIAL 27 8) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. The cylindrical smoke stack on the model has a height of 4 centimeters and a radius of 1.5 centimeters. What is the volume of the smoke stack on the actual ship? a)48∏ cubic meter b)64∏ cubic meter c)88∏ cubic meter d)72∏ cubic meter

28. CONFIDENTIAL 28 19) Natasha builds a model ship from a kit. She tries to picture what the actual ship looks like. The scale factor from the model to the actual ship is 200. The cylindrical smoke stack on the model has a height of 4 centimeters and a radius of 1.5 centimeters. What is the surface area of the smoke stack on the actual ship? a)48∏ square meter b)64∏ square meter c)88∏ square meter d)45∏ square meter

29. CONFIDENTIAL 29 20) A closed rectangular box has a height of 2 feet, a length of 4 feet, and a width of 4 feet. What is the surface area of the box? a)48 square feet b)64 square feet c)88 square feet d)45 square feet

30. You did a great job today!