Scale Drawings & Models 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 Measurements A 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 width Actual width--> 4 feet x feet <-----actual width 1x = 46.5 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 feet 4 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 6x = 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. 4 Step 1: Find the measure of the garden’s length on the drawing. Let x represent the length. drawing length--> .25in = x in <--drawing length actual length--> 2 ft 16ft <---actual length .2516 =2x 4 = 2x 2 = x On the drawing, the length is 2 inches

drawing width--> .25 in = w inches <--drawing width 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 .258 = 2w 2 = 2w 1 = w On the drawing the width is 1 inch.

8 ft 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 = 1cm 1.2 cm x cm 4.8x = 1.2 x = .25 The scale of the drawing is 1 cm = .25cm