Scale Factors

Scale Factors

GCSE(F),

A drawing, map or model does not normally show the actual size of the object (or area, in the case of a map). The drawing shows the item reduced down (made smaller) or enlarged (made larger). The amount by which the size is changed is known as the scale factor, and is shown as a ratio.

A scale of 1:100 means that the drawing is 1/100th of the size of the real thing. On a map, a scale of 1:10 000 means that every centimetre on the map is 10 000cm, or 100m, on the ground.

Examples

1. A map shows details where 2km represents 5cm. What is the scale of this map?

Answer: 1: 40 000

Change km to cm so that all measurements are in the same units:

2 x 1000 x 100 (convert km to cm) = 200 000cm.

The scale is 5 : 200 000,

simplify both sides by dividing by 5

1: 40 000

2. On a drawing, the length of a house is shown as 3.5cm. The scale of the drawing is 1: 150. What is the actual length of the house?

Answer: 5..25m

The multiplier is 3.5 รท 1 = 3.5.

Multiply 3.5 x 150 = 525cm, or 5.25m.