Question

map scale and proportion question?

Answer 1

The question is:
The scale of Map P is 1:60,000. A 2.52km footpath is represented by a line on Map P. The area of a pond on Map P is 9.5cm^2.
(i)Find, in cm, the length of the footpath on Map P.
(ii)Find, in km^2 ,the actual area of the pond.
(iii)The same footpath was represented by a length of 1.8cm on Map Q. Find the scale of Map Q in the form of 1:n .

Please explain your wokings to me, especially (iii). thanks :)

Answer 2

i) 1:60,000 means 1m on the map is 60,000m in real life. If you had a meter on the map, you would multiply by 60,000 to get the real size. Here, you divide the real size by 60,000 to get the map size

Answer 3

hey wait.. its 1cm : 60,000cm , not metres :)

Answer 4

ii) for area, it is the same thing, but 1:60,000 in two directions, so we multiply by 60,000 squared\[9.5*60,000^{2}=Area\] in cm^2
Divide by 100^2 to get m^2. Divide again by 1000^2 for km^2

Answer 5

it doesn't matter, as long as the units match : )
1cm:60,000cm is the same ratio as 1m:60,000m

Answer 6

iii) here we just need the ratio of map size to real life size, but the map size needs to be a 1.
1.8cm/2.52km = 1.8cm/252,000cm
Divide top and bottom by 1.8
1/(252,000/1.8)=1/140000 or 1:140,000

Answer 7

:O thanks, i get it now (: