Scale Drawing

Worked Exercise

- The distance between two villages is 6.4KM. On the map of the region this distance is represented by a line 1.6 cm long. What is the scale of the map?
- 1: 400000
- 1: 40000
- 1: 4000
- 1: 4

Working

Actual distance = 6.4 km

Drawing length = 1.6cm

1 cm on the map =^{6.4}/_{1.6}= 4km on the ground

But 1 km = (1000 x 100) cm

4km = 4 x 1000 x 100

= 400000cm

Therefore scale = 1: 400000

The correct answer is A (1: 400000)

- A rectangular field measures 105 m. On a scale drawing of the field, the longer side is 7cm.What is the measurement of the width on this scale drawing?
- 5 cm
- 50 cm
- 500 cm
- 7.35cm

Working

7 cm represents 105 m

1 cm represents (105 ÷ 7)

Scale used,

1 cm represents 15m

? 75m

=^{(75 x 1)}/_{15}5cm

The correct answer is 5cm (A)

- The scale on a plan is 1:20. How many cm will represent 1m on this plan?
- 50 cm
- 50 cm
- 5 cm
- 2 cm

Working

1 : 20 scale means 1 cm on a drawing represents 20 cm on the ground.

1 cm represents 20cm

? 100cm

=^{100}/_{20}= 5cm

The correct answer is C (5cm)

- A rectangular field measuring 720m by 550m is to be represented on a scale drawing using the scale 1: 10,000. What is the perimeter of the drawing in centimetres?
- 0.254
- 2.54
- 25.4
- 254

Working

1: 10000 means 1 cm on the map represents 10000 cm on the ground

If 1 cm = 10,0000cm

? = 72,000cm

= (^{72000}/_{10000}) cm

= 7.2cm

If 1cm = 10,000cm

= 55,000cm

= (^{55,000}/_{10,000}) cm

= 5.5cm

Perimeter

P = 2(L+W)

= 2 (7.2 + 5.5)

= 25.4 cm

The correct answer is (C)

- The scale of a map is 1: 50000. What is the length of this map of a road 20km long?
- 40cm
- 400 cm
- 4000 cm
- 4 cm

Working

Scale 1 : 50000 means 1cm on the map represents 50000 cm on the ground.

20 km = 20 x 1000 x 100

= 2000000 cm

50,000cm represents = 1 cm

2,000,000 represents = 2,000,000 ÷ 50,000

= 40cm

The correct answer is A (40 cm)

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