Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models Do Now Convert the following measurements. 1. 192 inches = feet 16 2. 18.5 feet = inches 222 3. 324 inches = feet 27 Hmwk: Wbk p 50

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models EQ: How do I use ratios and proportions in scale drawings? M7G3.b Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures

Insert Lesson Title Here Course 2 5-9 Scale Drawings and Scale Models Insert Lesson Title Here Vocabulary scale model scale factor scale scale drawing

Scale Models and Scale Drawings Course 2 5-9 Scale Models and Scale Drawings This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is . 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

Scale Models and Scale Drawings Course 2 5-9 Scale Models and Scale Drawings A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

1 unit on the drawing is 20 units. Scale Interpretation 1:20 1 unit on the drawing is 20 units. 1 cm:1 m 1 cm on the drawing is 1 m. in. = 1 ft in. on the drawing is 1 ft. 1 4 1 4

Additional Example 1: Finding a Scale Factor Course 2 5-9 Scale Drawings and Scale Models Additional Example 1: Finding a Scale Factor Identify the scale factor. Room Blueprint Length (in.) 144 18 Width (in.) 108 13.5 blueprint length room length 18 144 Write a ratio using one of the dimensions. = 1 8 = A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. Caution! 1 8 The scale factor is .

Additional Example 1: Using Proportions to Find Unknown Scales or Lengths A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? 1 cm x m 2 cm 8 m Set up proportion using scale length . actual length = 4 = x The scale is 1 cm:4 m.

The scale a:b is read “a to b The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.” Reading Math

The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? 4 cm 12 m Set up proportion using scale length . actual length 1 cm x m = 3 = x The scale is 1 cm:3 m.

Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? scale length actual length 1000 1 = 8 mm x mm x = 0.008 The actual length of the amoeba is 0.008 mm.

Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length? scale length actual length 10,000 1 = 1 mm x mm x = 0.0001 The actual length of the fiber is 0.0001 mm.

Insert Lesson Title Here Course 2 5-9 Scale Drawings and Scale Models Insert Lesson Title Here Identify the scale factor. Model Aircraft Blueprint Length (in.) 12 2 Wing span (in.) 18 3 blueprint length aircraft length 2 12 = 1 6 = The scale factor is . 1 6

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 5 1 poster photo = Write a proportion to find the length l. 36 l 5 1 = l = 7.2

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models poster photo 5 1 = 20.5 w Write a proportion to find the width w. 5 1 = w = 4.1 The photo is 7.2 in. long and 4.1 in. wide.

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Write a proportion to find the length l. l 45 = 1.5 1 l = 67.5 Multiply.

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models dollhouse blueprint 1.5 1 = w 24 1.5 1 Write a proportion to find the width w. = w = 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

Scale Drawings and Scale Models Course 2 5-9 Scale Drawings and Scale Models On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? 1.5 60 7.5 d = d = 300 The distance between the cities is 300 miles.

Insert Lesson Title Here Course 2 5-9 Scale Drawings and Scale Models Insert Lesson Title Here On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? 1 50 7 d = d = 350 The distance between the cities is 350 kilometers.

A model of a 27 ft tall house was made using a scale of 2 in. :3 ft A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model? 18 = h The height of the model is 18 in.

A model of a 24 ft tall bridge was made using a scale of 4 in. :2 ft A model of a 24 ft tall bridge was made using a scale of 4 in.:2 ft. What is the height of the model? 48 = h The height of the model is 48 in.

A model was built using the scale 2 cm:0. 01 mm A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object? x = 0.15mm

Scale Drawings and Scale Models Insert Lesson Title Here Course 2 5-9 Scale Drawings and Scale Models Insert Lesson Title Here Lesson Quiz: Part I Identify the scale factor. 1. Statue of Liberty Model Height (in.) 1,824 8 1 228 2. On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 144 inches, or 12 feet

Scale Drawings and Scale Models Insert Lesson Title Here Course 2 5-9 Scale Drawings and Scale Models Insert Lesson Title Here Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km

Lesson Quiz 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? 1 cm = 1.5 ft 1 4 5.5 in. 72 in.