1. Grade 8 Changing Dimensions
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2. Volume has increased 8 times by doubling the dimensions!
Building a Bigger Box:
Doubling the Volume of a Rectangular Prism. 6 3 2 4 1 2
1-2-3 box
2-4-6 box
Volume = 1 x 2 x 3 = 6 units3
Volume = 2 x 4 x 6 = 48 units3
Volume has increased 8 times by doubling the dimensions!
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3. Building a Bigger Box: Doubling the Volume of a Rectangular Prism.
We need boxes with volume = 12 units3 3 6 2 2 1 1
1-2-3 box
1-2-6 box
Volume = 1 x 2 x 3 = 6 units3
Volume = 1 x 2 x 6 = 12 units3
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Volume has doubled!

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 box to the box is 2 because each edge length of the box must be multiplied by 2 to get the corresponding edge length of the box.
The cost of packaging materials and finding enough landfill for garbage and waste materials is becoming a problem for many
communities. Some communities are looking at composting as a way to recycle garbage into productive soil. Composting is a method for turning organic waste into rich soil. Today, many people have compost boxes that break down kitchen waste quickly and with little odor. The secret is in the worms!
Remember: compost boxes are open on top!
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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 to the 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.)
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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.
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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
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8. Let us do some practice problems!

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?
32 ft3
38 ft3
36 ft3
None of the above.
a) 32 ft3
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10. 2) What happens to the volume of a rectangular box if its
dimensions are doubled?
The volume will be 4 times as great
The volume will be 6 times as great
The volume will be 8 times as great
The volume will be 10 times as great
c) The volume will be 8 times as great.
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11. 3) What are the dimensions of a box that is
similar to a box but has a volume of
10,368 cubic feet? What is the scale factor
from the box to the new box? 14 12 16
None of the above.
b) scale factor is 12.
(The scale
factor is 10,368 ÷ 6 = 1,728.We need to find
a number whose cube is 1,728.We know that
103 is 1,000, so it must be greater than 10 but
not much. 113 is 1,331, and 123 is 1,728, so the
scale factor is 12.The new box’s dimensions
are 12 feet by 24 feet by 36 feet.)
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12. 4) Sandra wants to build a compost box that will decompose 8 times garbage than the amount of the box. What are the dimensions of the new box?
6-4-6
2-2-6
8-4-2
2-4-6
d) 2-4-6
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13. What is the radius of the ball?
5) When a ball is immersed in water, it displaces 36π cubic centimeters of water.
What is the radius of the ball?
2cm
3 cm
4 cm
5 cm
b) 3cm
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14. 6) What are the dimensions of a box similar to a 1-2-3 box if the scale factor is 9? d)
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15. 7) What is the surface area of a compost box similar to a 1-2-3 box if the scale factor is 9?
1,382 square unit
1,296 square unit
1,282 square unit
1,482 square unit
b) 1,296 square unit
The surface area is
16 x 81 = 1,296 square feet, as the surface area of a box is 16 and the scale factor is 9
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16. 8) What is the volume of a compost box similar to a 1-2-3 box if the scale factor is 9?
4,354 cubic units
4,074 cubic units
4,370 cubic units
4,374 cubic units
d) 4,374 cubic units.
(the volume
is 6 x 729 = 4,374 cubic feet. As the volume of a box is 6 and the scale factor is 729)
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17. area of a 1-2-3 box is 16 square feet, so the
9) What are the dimensions of a compost box that is similar to a box but has a surface area of
1600 square feet? c)
(The surface
area of a box is 16 square feet, so the
scale factor from the small box to the large
box is 10.This means that the new box’s
dimensions are 10 feet by 20 feet by 30 feet.)
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18. 10)  What is the scale factor of a compost box that is similar to a box but has a surface area of
1600 square feet?   
16. 9.
20.
10.
d) 10.
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19. Assessment

20. 1) If you tripled each dimension of a 1-2-3 box,
what would happen to the volume?
It would be 27 times the original
It would be 4 times the original
It would be 8 times the original
It would be 25 times the original
a) It would be 27 times the original.
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21. 2) What happens to the surface area if the dimensions are quadrupled?
The surface area will be 14 times as great.
The surface area will be 16 times as great.
The surface area will be 9 times as great.
The surface area will be 4 times as great.
b) The surface area will be 16 times as great.
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22. 3) If the scale factor from a 1-2-3 box to a larger
box is 4, how many boxes will fit in the large box? 66 75 64 77
c) 64
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23. 4) Natasha builds a model ship from a kit
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?
50 m
25 m
36 m
40 in
a) 50 m
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24. 5) Natasha builds a model ship from a kit
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?
12 cm
14 cm
16 cm
15 cm
d) 15 cm
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25. 6) Natasha builds a model ship from a kit
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?
40 square meter
60 square meter
80 square meter
100 square meter
c) 80 square meter
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26. 7) Natasha builds a model ship from a kit
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?
radius = 3m; height = 8m
radius = 3m; height = 6m
radius = 2m; height = 8m
radius = 4m; height = 10m
c) radius = 3m; height = 8m
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27. 8) Natasha builds a model ship from a kit
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?
48∏ cubic meter
64∏ cubic meter
88∏ cubic meter
72∏ cubic meter
d) 72∏ cubic meter
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28. 19) Natasha builds a model ship from a kit
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?
48∏ square meter
64∏ square meter
88∏ square meter
45∏ square meter
a) 48∏ square meter
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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?
48 square feet
64 square feet
88 square feet
45 square feet
b) 64 square feet
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30. You did a great job today!