Map scales A scale drawing is a drawing

Map scales A scale drawing is a drawing in which all dimensions have been reduced in exactly the same proportion. For example, if a model boat is made to a scale of 1: 20 (1 to 20), this scale can be applied to any units, so that 1 mm measured on the model is 20 mm on the actual boat, 1 cm measured on the model is 20 cm on the actual boat, and so on. . . 1

Worked example a) If the 1: 20 model boat is 15 cm wide, how wide is the actual boat? b) If the boat has a mast of height 4 m, how high is the mast on the model? Solution: The scale is 1: 20. This means that every cm on the model is equivalent to 20 cm on the real boat. 2

Solution a) 1 cm on the model = 20 cm on the actual boat, so we calculate 15 cm x 20 = 300 cm. 15 cm on the model = 300 cm (3 m) on the actual boat b) 20 cm on the actual boat = 1 cm on the model, so we calculate 400 cm = 20 cm 20 400 cm (4 m) on the actual boat = 20 cm on the model 3

Sample question Now try the following question: The scale of a map is 1: 50 000 a) A distance is measured as 2 cm on the map. i) How many cm is this equivalent to in real life? 1 cm on the map represents 50 000 cm in real life. Therefore, 2 cm on the map represents 100 000 cm in real life. 4

Sample question ii) How many m is this equivalent to? To convert from cm to m, we divide by 100000 cm = 1000 m iii) How many km is this equivalent to? To convert from m to km we divide by 1000 m = 1 km. 5

Sample question b) What distance on the map will represent 5 km in real life? (Hint: Use your answers to part a) to help you!) In part a) we saw that 1 km in real life was equivalent to 2 cm on the map. Therefore, 5 km in real life is equivalent to 10 cm on the map. 6