SCALE DRAWING AND MODELS A scale drawing represents something that is too large or too small to be drawn or built at actual size. The scale of a model or drawing is the ratio of the length of the model or drawing to the actual length of the object. So, the scale gives the relationship between the drawing/model measure and the actual measure.

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The scale factor of a drawing or scale model is the scale written as a ratio without units in simplest form. Scale factors are always written so that the model length in the ratio comes first. The scale of a map is also a ratio. On a map with a scale of 1:100, every length of 1 unit on the map represents a length of 100 units on the ground.

It is your turn! 1) This is a model of a tractor built to scale 1:50. There is some information about the model. Calculate the actual length of: a. The diametre of the small wheel. b. The diametre of the large wheel. c. The length of the tractor. d. The height of the tractor. e. The length of the ladder.

2) This is a model of a tractor built to scale 1:32. There is some information about the model. Calculate the actual length of: a. The diametre of the large wheel. b. The diametre of the small wheel. c. The length of the tractor. d. The height of the tractor. e. The length of the side mirror.

3) This is a picture from a Matrioska which actual height is 14 cm. a. Measure the height of the picture and calculate the scale. b. There are five Matrioskas in a set. How tall would be the picture of the second one (with the scale of a) ) if it has an actual height of 10 cm?

4) What is the map scale if 80 km on the ground are represented by 2 cm on the map?

5) A map has the scale 3 : 700,000. What is the actual distance between two points which distance on the map is 12 cm?

6) Two people are at a distance of 1,500 m. How do you represent that distance on a map which scale is 1:6,000?

7) What is the map scale if 900 hm on the ground are represented by 5cn on the map?

8) What is the scale drawing if a 30 m building is represented by 15 cm? If I draw the same building using the scale 1:100, how will the picture be, greater or smaller? Why?

9) On a blueprint of scale 1 : 120, the area of a flat is 75 cm2. How many m2 has the actual flat? The rectangular kitchen measures on the plan 3cm width and 6 cm long. What is the actual area of the kitchen?

10) Find the actual distance between two towns if they are 12 cm far away on a map of scale 1 : 5,000,000.

11) A model of Pisa´s Tower has a scale model of 1:300. The model has a height of 18 cm. How long is the Pisa´s Tower?

12) The distance between Zaragoza and Valencia on a map is 60 cm. The map scale is 1 : 55,000. How many kilometres there are between Valencia and Zaragoza?

13) The length of the dining room on a blueprint is 5.6 cm. The scale is 1 : 100. What is the actual length of the dining room?

14) There are 600 km between Huelva and Madrid. What will the distance be on a map of scale 1 : 6,000,000?

15) A soccer ground measures 120 m long. We are going to make a model with a scale model of 1 : 250. Calculate the length of the model.

16)

The blueprint of a flat has a scale of 1 : 120. The width of the kitchen is 4.5 cm on the blueprint, and the actual width is 3.6 m. Is the blueprint well built?

17) The length of the side of the base of The Khufu’s pyramid measures 240 m. There is a model in which that side measures 16 cm. a. What is the scale model? b. Calculate the model height if the actual height is 159 m.

18) Carla has made a blueprint of her class using a scale of 1 : 100. Calculate the actual length and width of the class if it measures on the blueprint 4.2 and 2.8 respectively.

19) Jose has a blueprint of his future house. His room measures 1.5 cm by 2 cm on the blueprint. Calculate the actual measures if the scale is 1 : 200.

20)

Two villages are 7.5 cm apart on a map of scale 1 : 200,000. Calculate

the actual distance between them, in kilometres.

21) Laura is going to build a model of The Eiffel Tower using a scale of 1 : 48. Calculate the height of the model if the actual height of The Eiffel Tower is 324 m.

22)

We have the blueprint of a house. Calculate:

a. The scale of the blueprint. b. The dimensions, width and length, of the single room and of the kitchen.