Scales are related to ratios
Scales are used on maps, drawings etc., as well as for scale models.
There are two ways the scale could be stated
As a straightforward relation between the dimensions
on the map/drawing etc. and the real-life dimensions.
This particular ratio is the same as '2 cm to 1 km' because
= 100 000 cm
= 1 kilometer
Length 366 mm, Scale 1:87
Length 406 mm, Scale 1:600
Length 425 mm, Scale 1:144
Past Exam Questions
Some friends are planning a camping holiday in May. The table shows information on the prices of some of the campsites available
There are 4 people in the group and they are taking 2 tents for 3 nights in May. They calculate that Roversí Rest is the cheapest for them and Vibram Farm would be the most expensive.
1. How much would they save by going to Roversí Rest rather than Vibram Farm?
- A £6.50
- B £8.50
- C £19.50
- D £25.50
There is a brilliant surfing beach 25 kilometres from Roversí Rest but no one can
remember its name.
One of the friends has a map with a scale of 2cm to 5km and he measures the
distance from Roversí Rest on the map to 4 local beaches.
Which one is the surfing beach?
- A Blackrock Sands 2 cm
- B Gull Cove 5 cm
- C St Peter's Bay 7 cm
- D Whitesands 10 cm
3. Their car uses 1 litre of petrol to travel 14.8 kilometres. The campsite is
88 kilometres away from their home town. They estimate how much fuel they will
need for the trip there and back.
Which of these 4 attempts gives the closest estimate of the fuel required?
- A 90 ÷ 15 = 6 litres
- B 90 ÷ 10 = 9 litres
- C 180 ÷ 15 = 12 litres
- D 180 ÷ 10 = 18 litres
4. One of the items on their list of supplies is 6 yoghurts. The supermarket has
several special offers.
Which would work out cheapest?
- A Original price 26p: buy one, get a second half-price
- B Original price 26p: buy two, get the third free
- C Original price 27p: one third off
- D Original price 28p: 25% off
An architect is making a scale model of a new house from a drawing. One of the dimensions on the drawing shows that the height of the real house is 12.5 metres. What scale does the architect need to work to, if the height of the model house has to be 2.5 centimetres?
- A 1 : 5
- B 1 : 50
- C 1 : 100
- D 1 : 500
Holly is looking at a scale model of the Sports Hall where she works. The model is a cuboid and is 1 metre long, 50 centimetres wide and 200 millimetres high.
a) What are the dimensions of the Sports Hall in meters, if the scale of the model is 1:50?
b) It costs 0.03p per cubic metre each hour to heat the Hall. The Hall is open every day and heated for 8 hours each day. How much would it cost to heat the Hall for one week?
c) Holly orders new badminton nets for the 4 badminton courts. Each court requires 8 meters of netting, which costs £2.67 per meter plus VAT at 17.5%. What is the cost of replacing all the netting?
This scale drawing shows the front view of a garage.
b) Work out the actual area of the garage door (on the original diagram the length and width were both 2.5 cm.
c) The garage roof is a rectangle 6 m long. Draw a scale diagram of the garage roof, to a scale of 1:80.