Chapter 6 Lesson 3Scale Drawings &

Modelspgs. 276-280

What you will learn:Use scale drawings

Construct scale drawings

Vocabulary• Scale drawing/scale model (276): is

used to represent an object that is too large or too small to be drawn or built at actual sizes

• Scale (276): gives the relationship between the measurements on the drawing or

model and the measurements of the real object

• Scale factor (277): the ratio of a length on a scale drawing or model to the corresponding length on the real object

Scale

Example:1 inch = 3 feet

(One inch represents an actual distance of 3 feet)

1:24(1 unit represents an actual distance of 24

units)

Scale Factor

Example: Suppose a scale model has a scale of 2 inches = 16 inches. The scale factor is 2 or 1 16

8

The lengths and widths of objects of a scale drawing or model are proportional to the lengths and widths of the actual object.

Example 1: Find Actual

MeasurementsA set of landscape plans shows a flower bed that is 6.5

inches wide. The scale on the plans is 1 inch = 4 feet.

What is the width of the actual flower bed?Let x represent the actual width of the flower bed.

Write and solve a proportion. Plan width----> 1 inch = 6.5 inches<---plan widthActual width--> 4 feet x feet <-----actual width 1x = 46.5 cross products

x= 26 The actual flower bed width is 26 feet.

From the last example, what is the scale factor?

To find the scale factor, write the ratio of 1 inch to 4 feet in simplest form.

1inch = 1 inch Convert 4 feet4 feet 48 inches to inches

The scale factor is 1 . That is , each 48

measurement on the plan is 1 the actual measurement. 48

Example 2: Determine the Scale

In a scale model of a roller coaster, the highest hill has a height of 6 inches. If the actual height of the hill is 210 feet, what is the scale of the model?

Model height---> 6 inches = 1 inch <--model height

Actual height--->210 feet x feet <--actual height

6x = 210

6x = 210 x= 35 6 6 So, the scale is 1” =

35 feet

Example 3: Construct a Scale Drawing

A garden is 8 feet wide by 16 feet long. Make a scale drawing of the garden that has a scale of 1 in. = 2ft.

4Step 1: Find the measure of the garden’s length on the

drawing. Let x represent the length.drawing length--> .25in = x in <--drawing lengthactual length--> 2 ft 16ft <---actual length .2516 =2x

4 = 2x

2 = xOn the drawing, the length is 2 inches

• Step 2: Find the measure of the garden’s width on the drawing. Let w represent the width.

drawing width--> .25 in = w inches <--drawing width

actual width ---> 2 feet 8 feet <---actual width

.258 = 2w 2 = 2w

1 = wOn the drawing the width is 1 inch.

• Step 3: Make the scale drawing. Use 1/4” grid paper. Since 2” = 8 squares and 1

inch = 4 squares, draw a rectangle that is 8 squares by 4 squares.

<------------------------ 16 ft--------------------->

8 ft

Your Turn!

On a set of architectural drawings for an office building, the scale is 1/2” = 3 feet. Find the actual length of each room.

Lobby: 2 inches

Cafeteria: 8.25 inches

.5” = 2” 3ft x ft .5x = 6 The actual length x = 12 of the lobby is 12 ft

.5” = 8,25”3ft x ft The actual length of the.5x = 24.75 cafeteria is 49.5 feet x = 49.5

Your Turn, Again!

In an illustration of a honey bee, the length of the bee is 4.8 cm. The actual size of the honeybee is 1.2 cm. What is the scale of the drawing?

4.8 cm = 1cm1.2 cm x cm 4.8x = 1.2 x = .25

The scale of the drawing is 1 cm = .25cm

• Extra Practice sheets are by the door on your way out, be sure to grab one!

• Quiz over 6-1 thru 6-3 Tomorrow!