Tutor’s Toolkit: Application of Number

Carrying Out Calculations

C6	Work out dimensions from scale drawings

C6.1	Work out dimensions from scale drawings

Scope: 

Students need to be able to:
•	Calculate dimensions on the object.
•	Calculate dimensions on the plan.
•	Change units.

What students need to know:

Working with scale drawings uses just the same procedure as converting units and currencies (Refer to Carrying Out Calculations, Section C4). We are given a conversion factor (the scale) and we need to multiply to find the larger unit (normally the real object or the ground in the case of a map). Alternatively, we divide when finding the smaller unit (the model or distances on the map).

It is very likely that units will need to be changed. Distances on maps may be a few centimetres, but they could represent many kilometres on the ground.

Example Question:

A map is drawn to a scale of 1:25,000. 
(a)	On the map, the field measures 2cm long. How long is the field on the ground. Give your answer in metres.
(b)	A straight road is 2.5km long. How long will it be on the map?

Solutions:

(a)	To find the larger unit, we multiply:
2  25,000 = 50,000cm
50,000cm = 50,000  100 = 500m

(b)	2.5km = 2.5  1000 = 2,500m = 2,500  100 = 250,000cm
	To find the smaller unit, we divide:
	250,000  25,000 = 10cm