Scale Drawings & Models What you will learn: Use scale drawings Construct scale drawings

Vocabulary Scale drawing/scale model: is used to represent an object that is too large or too small to be drawn or built at actual sizes Scale: gives the relationship between the measurements on the drawing or model and the measurements of the real object Scale factor: 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 1:24 (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.

Find Measurements Landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4’ Q: 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 Actual width--> 4 feet x feet 1  x = 4  6.5 {cross multiply!} 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 4 feet 48 inches {Convert 4’ to inches} The scale factor is 1/48 . That is , each measurement on the plan is 1/48th of the actual measurement.

Determine the Scale Model height---> 6 inches = 1 inch Q: 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 Actual height--->210 feet x feet 6x = 210 6x = 210 x= 35 6 6 So, the scale is 1” = 35 feet

Construct a Scale Drawing Q: 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 actual length--> 2 ft 16ft .25  16 =2  x 4 = 2x 2 = x On the drawing, the length is 2 inches

Construct a Scale Drawing Step 2: Find the measure of the garden’s width on the drawing. Let w represent the width. drawing width--> .25 in = w inches actual width ---> 2 feet 8 feet .25  8 = 2  w 2 = 2w 1 = w On the drawing the width is 1 inch.