WRITING THE GIVEN SCALES AS RATIO AND FIND SCALE FACTOR

When designing a house it would be a ridiculous for an architect to draw a full plan.

Instead the architect draws a smaller diagram in which all measurement have been divided by the same factor and that is called scale factor.

In scale diagrams:

(i)  All lengths have been changed by the same scale factor.

(ii)  All angles are unaltered

Example 1 :

On a scale diagram 1 cm represents 20 m.

a) Write the scale as a ratio.

b) What is the scale factor?

Solution :

1 m  =  100 cm

20 m  =  20 x 100  ==>  2000 cm

(a)  1 : 2000

(b)  So, the scale factor is 2000.

Example 2 :

1 cm represents 10 m

Solution :

1 m  =  100 cm

1 cm : 10 m  ==>  1 cm : 100 cm

So, the scale factor is 100.

Example 3 :

1 cm represents 50 km

Solution :

100 cm  =  1 m

1000 m   =  1 km

1 km  =  100000 cm

50 km  =  5000000 cm

1 cm : 50 km  =  1 : 5000000

So, the scale factor is 5000000.

Example 4 :

1 mm represents 2 m

Solution :

10 mm  =  1 cm

100 cm  =  1 m

2 m  =  1000 mm

1 mm : 2 m  =  1 : 1000

So, the scale factor is 1000.

Example 5 :

1 cm represents 250 km

Solution :

100 cm  =  1 m

1000 m   =  1 km

1 km  =  100000 cm

250 km  =  25000000 cm

1 cm : 250 km  =  1 : 25000000

So, the scale factor is 25000000.

Example 6 :

1 mm represents 5 m

Solution :

10 mm  =  1 cm

100 cm  =  1 m

1 m  =  1000 mm

5 m  =  5000 mm

1 mm : 5 m  =  1 mm : 5000 mm

So, the scale factor is 5000.

Example 7 :

1 cm represents 200 km.

Solution :

100 cm  =  1 m

1000 m  =  1 km

1 km  =  100000 cm

200 km  =  20000000

1 cm : 200 km  =  1 : 20000000

So, the scale factor is 20000000.

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