Using the Scale of a Map © T Madas

What is the direct air distance from London to Athens? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 17.6 cm x 19 500 000 = 343 200 000 cm = 3 432 000 m = 3 432 km © T Madas

What is the direct air distance from London to Budapest? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10.5 cm x 19 500 000 = 204 750 000 cm = 2 047 500 m ≈ 2 048 km © T Madas

What is the true distance for every mm on this map? x 19 500 000 = 19 500 000 mm = 19 500 m = 19.5 km © T Madas

What is the direct air distance from London to Warsaw? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 3.5 cm = 300 miles x 3.03 x 3.03 10.6 cm = ? miles 909 10.6 ÷ 3.5 ≈ 3.03 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas

What is the direct air distance from London to Berlin? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 3.5 cm = 300 miles x 1.97 x 1.97 6.9 cm = ? miles 591 6.9 ÷ 3.5 ≈ 1.97 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas

Another Example Scale 1 : 125 000 © T Madas

Find the distance between the 2 points on this map 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Scale 1 : 125 000 6.8 cm x 125 000 = 850 000 cm = 8 500 m = 8.5 km © T Madas

20 km Another Example © T Madas

Find the distance between the 2 points marked on this map 20 km 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 5.3 cm = 20 km x 2.15 x 2.15 11.4 cm = ? km 43 11.4 ÷ 5.3 ≈ 2.15 © T Madas

Floor Plans © T Madas

3.328 m The diagram opposite shows an architect’s floor plan for a bathroom. The scale of this plan is 1 : 32 Calculate the internal width and length of this bathroom and the width of the door [in m] door 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10.4 cm x 32 = 332.8 cm = 3.328 m © T Madas

3.328 m The diagram opposite shows an architect’s floor plan for a bathroom. The scale of this plan is 1 : 32 Calculate the internal width and length of this bathroom and the width of the door [in m] door 3.168 m 10.4 cm x 32 = 332.8 cm = 3.328 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 9.9 cm x 32 = 316.8 cm = 3.168 m © T Madas

3.328 m The diagram opposite shows an architect’s floor plan for a bathroom. The scale of this plan is 1 : 32 Calculate the internal width and length of this bathroom and the width of the door [in m] door 3.168 m 10.4 cm x 32 = 332.8 cm = 3.328 m 9.9 cm x 32 = 316.8 cm = 3.168 m 2.5 cm x 32 = 80 cm = 0.8 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas

Another Example © T Madas

The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms The scale of this plan is 1 : 40 Calculate the internal dimensions of the two rooms in metres Desk A Desk B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 9.4 cm x 40 = 376 cm = 3.76 m © T Madas

The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms The scale of this plan is 1 : 40 Calculate the internal dimensions of the two rooms in metres Desk A Desk B 9.4 cm x 40 = 376 cm = 3.76 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 7.1 cm x 40 = 284 cm = 2.84 m © T Madas

The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms The scale of this plan is 1 : 40 Calculate the internal dimensions of the two rooms in metres Desk A Desk B 3.76 m by 2.84 m 9.4 cm x 40 = 376 cm = 3.76 m 3.76 m by 3.28 m 7.1 cm x 40 = 284 cm = 2.84 m 8.2 cm x 40 = 328 cm = 3.28 m © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

© T Madas

Scale 1 : 20 : 13 cm 9 cm ? tallest average shortest The average height of a human adult male is 180 cm and this is shown below using the scale 1 : 20 Using the same scale, the tallest and the shortest man in the world are also drawn for comparison. 1. What is the actual height of the tallest man in the world? 2. If the actual height of the shortest man in the world is 70 cm what is his height in the drawing? Scale 1 : 20 drawing 1 1 cm 13 cm : actual 20 20 cm 260 cm 13 cm x13 x13 9 cm ? tallest average shortest © T Madas

Scale 1 : 20 : 13 cm 9 cm 3.5 cm 70 cm ? tallest average shortest The average height of a human adult male is 180 cm and this is shown below using the scale 1 : 20 Using the same scale, the tallest and the shortest man in the world are also drawn for comparison. 1. What is the actual height of the tallest man in the world? 2. If the actual height of the shortest man in the world is 70 cm what is his height in the drawing? Scale 1 : 20 drawing 1 1 cm 2 cm 3 cm 4 cm : actual 20 20 cm 40 cm 60 cm 80 cm 13 cm 9 cm 3.5 cm 70 cm ? tallest average shortest © T Madas

© T Madas

A model of a helicopter is made to a scale of 2 cm to 1 m. 1. Calculate the actual span of the helicopter’s rotor in m, if it measures 16 cm in the model. 2. What is the span of the tail rotor in the model in cm, if its actual span is 2.5 m? Model cm 2 16 : Actual m 1 8 x 8 x 8 The rotor has an actual span of 8 m © T Madas

A model of a helicopter is made to a scale of 2 cm to 1 m. 1. Calculate the actual span of the helicopter’s rotor in m, if it measures 16 cm in the model. 2. What is the span of the tail rotor in the model in cm, if its actual span is 2.5 m? Model cm 2 5 : Actual m 1 2.5 x 2.5 x 2.5 The tail rotor has a span of 5 cm in the model © T Madas

© T Madas

9 cm cm m The diagram opposite shows an architect’s plan for a bedroom The scale of this plan is 1 : 36 Calculate the internal area of this bedroom in m2, correct to 2 d.p. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 9 cm x 36 = 324 cm = 3.24 m © T Madas

3.24 m The diagram opposite shows an architect’s plan for a bedroom The scale of this plan is 1 : 36 Calculate the internal area of this bedroom in m2, correct to 2 d.p. 9 cm x 36 = 324 cm 4.68 m = 3.24 m 13 cm x 36 = 468 cm = 4.68 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 © T Madas

3.24 m The diagram opposite shows an architect’s plan for a bedroom The scale of this plan is 1 : 36 Calculate the internal area of this bedroom in m2, correct to 2 d.p. 9 cm x 36 = 324 cm 4.68 m = 3.24 m A = 15.16 m2 (2 d.p.) 13 cm x 36 = 468 cm = 4.68 m 3.24 x 4.68 = 15.1632 m2 © T Madas

© T Madas

1 cm = 1 : 200 m 20000 cm 20000 1 inch = 1.5 inch = 2.54 cm 3.81 cm The scale of a town map is 1 cm = 200 m On this map, the town hall is 1½ inches away from the local church. 1. Write down the scale of this map as a unit ratio, in the form 1 : … 2. Calculate the distance between the town hall and the local church, correct to the nearest 10 metres 1 cm = 1 : 200 m 20000 cm 20000 1 inch = 1.5 inch = 2.54 cm 3.81 cm 3.81 cm x 20000 = 76200 cm = 762 m ≈ 760 m © T Madas

© T Madas

The length of a model helicopter is 40 cm. The actual length of the helicopter is 18.4 m 1. Write down the scale of this model as a unit ratio, in the form 1 : … 2. Calculate the actual span of the helicopter’s rotor in m, if it measures 35 cm in the model. 3. What is the span of the tail rotor in the model in cm, if its actual span is 2.07 m? 40 cm = 1 : 18.4 m 1840 cm 46 35 cm x 46 = 1610 cm = 16.1 m 2.07 m ÷ 46 = 0.045 m = 4.5 cm © T Madas

© T Madas