### 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   If we wish to give this answer in instead, we know 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  