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Lesson 6-4: Scale Drawings and Models

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Key Definitions:

• Scale drawing or model: used to represent an object that is too small or too large to be drawn or built at actual size

o Examples: model airplanes, buildings, and cars; blueprints or other plans for construction; maps

o The lengths and widths of the model are _____________________to those of the actual figure.

• Scale: determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object

o Example: 1 inch = 3 feet (1 inch on the _________ represents an __________ length of 3 feet)

o Always make sure the scale is written as 1 unit = x units

o Drawing measurement = actual measurement

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• Scale factor: when the scale is written as a fraction in simplest form, with the same units of measure

o Example 1: Suppose a scale model has a scale of 2 inches = 16 inches, the scale factor is [pic], which means that the scale model is one-eighth of the actual size.

o Example 2: Suppose a scale model has a scale of 1 inch = 3 feet, the scale factor is [pic]. (The 36 comes from the fact that there are 36 inches in 3 feet.)

1) On a scale model of a building, the highest point 2) On a scale model of a building, the highest point

of the building is 14 inches. The actual height of of the building is 14 inches. The actual height of

the building is 175 feet. What is the scale of the the building is 175 feet. What is the scale

model? factor?

3) On a set of landscape plans for a new garden, 4) On a set of landscape plans for a new garden, the

the length of the garden is 18.5 inches. If the actual length of the garden is 18.5 inches. The actual

length of the garden is 111 feet, what is the scale length of the garden is 111 feet. What is the

of the plans? scale factor?

5) If the scale of a blueprint of a building is 6) Drew is putting in a new patio in his backyard.

1 inch = 8 feet. What is the scale factor? On the set of plans that he has made, ½ inch

represents 8 feet. What is the scale for his plans?

7) In an illustration in a textbook, the length of 8) If the scale is 10 inches = 1 foot. What is the

a fly is 4 inches. The actual size of an scale factor?

average fly is 0.2 inches. What is the scale of

the illustration?

On a set of architectural drawings for a new school building, the scale is ¼ inch = 2 feet. Write and solve a proportion to find each of the missing lengths of the rooms in the table below.

|Room |Drawing Length |Actual Length |

|Lobby |__________ inches |16 feet |

|Science Lab |1.5 inches |_________ feet |

|Band Room |4 inches | |

|Auditorium | |56 feet |

|Gymnasium |13 inches | |

|Teacher’s Lounge |1.75 inches | |

|Cafeteria | |48 feet |

Lobby Science Lab

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Word Problems

9) A set of landscape plans shows a flower 10) The blueprint of a building shows that its

bed that is 6.5 inches wide. The scale on height is 11.4 inches. If the scale on the

the plans is 1 inch = 4 feet. What is the width blueprint is 1 inch = 6 feet, what is the

of the actual flower bed? height of the actual building?

11) The penny coin has a diameter of ¾ inch. 12) The pillars of the World War II memorial in

Suppose a scale drawing has a diameter of 3 cm. Washington, D.C., are 17 feet tall. A scale

What is the scale of the model? model of the memorial has pillars that are 5

inches tall. What is the scale of the model?

REMEMBER: Scale is 1 in = 40 miles or 1 cm = 100 km AND scale factor is a fraction.

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SCALE

What is the scale factor?

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