Common Map Scale Questions

In this O-level Math revision note, we will explore some common Map Scale questions and how to solve them.

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map scale questions

 

Using Map Scale to Calculate Distances and Lengths

  • A map scale refers to the relationship between a distance on the map and the corresponding actual distance. A map scale is usually written as a ratio, in the format

In the format 1 : n, no measurement units are included and it is interpreted as:
1 unit length on the map corresponds to n units of actual distance on the ground.

For instance, a map scale of 1 : 20 000 refers to
1 cm on the map = 20 000 cm on the ground
= 0.2 km on the ground

 

  • Note that a map can also be expressed as a representative fraction (RF), 1/n.

Map Scale Questions Type 1: Finding Map Scale

1. Write the following map scales in the form of 1 : n, where n is a whole number.
(a) 2 cm represents 6 m       (b) 5 cm represents 400 km
2 cm : 600 cm                              5 cm : 40 000 000 cm
1 cm : 300 cm                              1 cm : 8 000 000 cm
Ans: 1 : 300                                  Ans: 1 : 8 000 000

 

2. Given that the actual distance of 8 km is represented by 10 cm on a map, state the value of n when the map scale is expressed as a representative fraction, 1/n.10 cm : 8 km

10 cm : 800 000 cm
1 cm : 80 000 cm
Ans: n = 80 000

Map Scale Questions Type 2: Finding actual distance given length on map

Given that the scale of a map is 1 : 15 000. Find
(a) the actual distance, in m, for a length of 10 cm on the map.
(b) the actual distance, in km, for a length of 8 cm on the map.

(a)
1 cm : 15 000 cm
1 cm : 150 m
10 cm : 10 × 150 m
= 1500 m (ans)

(b)
1 cm : 1 500 m
1 cm : 0.15 km
8 cm : 8 × 0.15 km
= 1.2 km (ans)

 

Map Scale Questions Type 3: Finding length on map given actual distance

Given that the scale of a map is 1 : 50 000. Find the length on the map, in cm,
(a) for an actual distance of 150 m.
(b) for an actual distance of 20 km.

(a)
1 cm : 50 000 cm
1 cm : 500 m
1/500×150 cm : 150 m
= 0.3 cm (ans)

(b)
1 cm : 500 m
1 cm : 0.5 km
1/0.5×20 cm : 20 km
= 40 cm (ans)

Using Map Scale to Calculate Areas

  • If the map scale is given as m : n, then the ratio of the area measured on the map to the actual area on the ground is

This means each m2 square unit of area on the map corresponds to n2 square units of actual distance on the ground.
For instance, given a map scale of 1 cm to 4 km, we have the map area scale of 1 cm2 : 16 km2 .
1 cm2 on the map = 16 km2 on the ground.

 

  • When given a map area scale of m2 : n2, we can obtain the map scale for length by square rooting both sides of the ratio to get m : n.

Map Scale Questions Type 4: Finding actual area given map area

Given that the scale of a map is 1 : 30 000, find
(a) the actual area, in m2, if the map area is 4 cm2,
(b) the actual area, in km2, if the map area is 25cm2

 

(a)
1 cm : 30 000 cm
1 cm : 300 m (Length)
1 cm : 90 000m2 (Area)
4 cm : 4 × 90 000 m2
         = 360 000 m2 (ans)

(b)
1 cm : 300 m
1 cm : 0.3 km (Length)
1 cm : 0.09 km2 (Area)
25 cm : 25 × 0.09 km2
= 2.25 km2 (ans)

 

Map Scale Questions Type 5: Finding map area given actual area

Given that the scale of a map is 1 : 25 000, find the map area, in cm2,
(a) if the actual area is 5000 m2,
(b) if the actual area is 25 km2.

(a)
1 cm : 25 000 cm
1 cm : 250 m (Length)
1 cm2 : 62 500 m2 (Area)
1/62500×5000 cm2 : 500 m2
= 0.08 cm2 (ans)

(b)
1 cm : 250 m
1 cm : 0.25 km (Length)
1 cm2 : 0.0625 km2 (Area)
1/0.0625×25 cm2 : 25 km2
= 400 cm2 (ans)

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