Question 1174278: a map is drawn to a scale of 1:5000 on the map, a village has an area of 6cm2. find the true area of the village in hectare
Found 3 solutions by ewatrrr, greenestamps, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
a map is drawn to a scale of 1:5000 on the map, a village has an area of 6cm^2.
find the true area of the village in hectare
Letting A represent that true area sets up the Proportion:
Scale represented as 5000^2 for Area.
 |Cross Multiplying to Solve
A =6(25(10^6)) ⇒ A = 150(10^6) cm^2 = 1.5(10^8)
***** Hectare = 1x10^8 cm^2 *****
A =  = 1.5 Hectares
Wish You the Best in your Studies.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The other tutor used an incorrect linear conversion. Area is measured in square units....
6cm^2 on the map for the village represents an actual area of 6*5000^2 = 150,000,000 cm^2.
One hectare is 10,000 cm^2; the area of the village is 150,000,000/10,000 = 15,000 hectares, which is 150 square kilometers.
Quite a large "village"....
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Solutions of BOTH tutors @greenestamps and @ewatrrr are incorrect.
I came to bring the correct solution.
The area of the real object is the area on the map multiplied by the SQUARE of the scale factor.
So, the area of the village is 6 * 5000^2 = 150000000 square centimeters.
1 square meter = 100^2 = 10000 square centimeters.
Therefore, the area of the village is 15000 square meters.
1 hectare is 100 meters x 100 meters = 10^4 square meters.
Therefore, the area of the village is 1.5 hectares.
Quite reasonable value.
Solved.
|
|
|
