CONFIDENTIAL 1

Grade 8 Grade 8

Changing Changing DimensionsDimensions

Building a Bigger Box:Building a Bigger Box:• Doubling the Volume of a Rectangular Prism.

CONFIDENTIAL 2

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1-2-3 box 2-4-6 box

Volume = 1 x 2 x 3 = 6 units3Volume = 2 x 4 x 6 = 48 units3

Volume has increased 8 times by doubling the dimensions!Volume has increased 8 times by doubling the dimensions!

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Building a Bigger Box:Building a Bigger Box:• Doubling the Volume of a Rectangular Prism.• We need boxes with volume = 12 units3

CONFIDENTIAL 3

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1-2-3 box 1-2-6 box

Volume = 1 x 2 x 3 = 6 units3Volume = 1 x 2 x 6 = 12 units3

Volume has doubled!Volume has doubled!

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Scaling Up the Compost Box: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 4Remember: compost boxes are open on top!Remember: compost boxes are open on top!

Scaling Up the Compost Box: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

Building Model Ships: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

Building Model Ships: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

Let us do some practice problems!

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 ft3

b) 38 ft3

c) 36 ft3

d) None of the above.

a) 32 ft3

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 greatb) The volume will be 6 times as greatc) The volume will be 8 times as greatd) The volume will be 10 times as great

c) The volume will be 8 times as great.

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a) 14b) 12c) 16d) None of the above.

3) What are the dimensions of a box that issimilar to a 1-2-3 box but has a volume of10,368 cubic feet? What is the scale factor

from the 1-2-3 box to the new box?

b) scale factor is 12.(The scale

factor is 10,368 ÷ 6 = 1,728.We need to finda number whose cube is 1,728.We know that103 is 1,000, so it must be greater than 10 butnot much. 113 is 1,331, and 123 is 1,728, so the

scale factor is 12.The new box’s dimensionsare 12 feet by 24 feet by 36 feet.)

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) 6-4-6b) 2-2-6c) 8-4-2d) 2-4-6

d) 2-4-6

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5) When a ball is immersed in water, it displaces 36π cubic centimeters of water.What is the radius of the ball?

a) 2cmb) 3 cmc) 4 cmd) 5 cm

b) 3cm

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6) What are the dimensions of a box similar to a 1-2-3 box if the scale factor is 9?

d) 9-18-27

a) 10-25-36b) 10-9-15c) 10-18-24d) 9-18-27

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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 unitb) 1,296 square unitc) 1,282 square unitd) 1,482 square unit

b) 1,296 square unitThe surface area is

16 x 81 = 1,296 square feet, as the surface area of a 1-2-3 box is 16 and the scale factor is 9

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 unitsb) 4,074 cubic units c) 4,370 cubic units d) 4,374 cubic units

d) 4,374 cubic units.(the volume

is 6 x 729 = 4,374 cubic feet. As the volume of a 1-2-3 box is 6 and the scale factor is 729)

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) 10-25-35b) 20-20-36c) 10-20-30d) 10-50-40

c) 10-20-30(The surface

area of a 1-2-3 box is 16 square feet, so thescale factor from the small box to the large

box is 10.This means that the new box’sdimensions are 10 feet by 20 feet by 30 feet.)

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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.

d) 10.

Assessment

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 originalb) It would be 4 times the originalc) It would be 8 times the originald) It would be 25 times the original

a) It would be 27 times the original.

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2) What happens to the surface area if thedimensions 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.

b) The surface area will be 16 times as great.

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3) If the scale factor from a 1-2-3 box to a largerbox is 4, how many 1-2-3 boxes will fit in the large box?

a) 66 b) 75c) 64d) 77

c) 64

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 mb) 25 mc) 36 md) 40 in

a) 50 m

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 cmb) 14 cmc) 16 cm d) 15 cm

d) 15 cm

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?

c) 80 square meter

a) 40 square meterb) 60 square meterc) 80 square meterd) 100 square meter

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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?

c) radius = 3m; height = 8m

a) radius = 3m; height = 8mb) radius = 3m; height = 6mc) radius = 2m; height = 8md) radius = 4m; height = 10m

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?

d) 72∏ cubic meter

a) 48∏ cubic meterb) 64∏ cubic meterc) 88∏ cubic meterd) 72∏ cubic meter

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

a) 48∏ square meterb) 64∏ square meterc) 88∏ square meterd) 45∏ square meter

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?

b) 64 square feet

a) 48 square feetb) 64 square feetc) 88 square feetd) 45 square feet

You did a great job today!