### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Areas and Volumes in Map Scale Problems

When the scale in the map is , the area scale is : and the volume scale is .
Also , squaring both sides gives

Cubing both sides gives

## More examples

A map is drawn to a scale of .
Calculate the actual length, in metres, of a canal which is long on the map
The actual area of a region is . What is its area in on the map?

Solution:
map/actual
Map given is long, substituting in the above gives
5cm/actual
Actual

since .
Map/Actual Squaring gives
Given actual area
Now so
Map
Map

So, { 1m }^{ 2 }={ 100 }^{ 2 }{ cm }^{ 2 }
And, therefore area on the map

A map is drawn to a scale of
The actual volume of a dam is . What is its volume in on the map.
Solution:

Since we are dealing with volume, we cube both sides

Given the actual volume of the dam , substituting

Map

Now

Map

An actual area of is represented by an area of on a map. Find the scale to which this map is drawn.

Solution:
since
Because this is an area scale, (squared) we take the square root of

The scale used is

A map is drawn to a scale of .
Find the area in of a village which is represented on the map by an area of .

Solution:

Squaring,
We are given an area on the map . We substitute in the above:

Actual

Now
So, .
Therefore, the actual area of village, in , is
.

On a plan, a piece of land is represented by an area of dimension . Given that a scale of to is used, find the actual area of the piece of land, giving an answer in .

Solution:
Area on the map

Scale:
Squaring gives
Substituting Map gives

Actual
Now,
So, .
Therefore, the actual area of land