Post on 03-Jan-2016
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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.
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
CONFIDENTIAL 11
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?
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
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) 2cmb) 3 cmc) 4 cmd) 5 cm
CONFIDENTIAL 14
6) What are the dimensions of a box similar to a 1-2-3 box if the scale factor is 9?
a) 10-25-36b) 10-9-15c) 10-18-24d) 9-18-27
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 unitb) 1,296 square unitc) 1,282 square unitd) 1,482 square unit
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
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
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.
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
CONFIDENTIAL 21
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.
CONFIDENTIAL 22
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
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
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
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 meterb) 60 square meterc) 80 square meterd) 100 square meter
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 = 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?
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 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?
a) 48 square feetb) 64 square feetc) 88 square feetd) 45 square feet
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