SOLUTION: 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

Algebra.Com
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.



RELATED QUESTIONS

A map is drawn to a scale of 1 : 25000 (a) The distance between two towns on the map is... (answered by Theo)
if the scale of a map is 1:25000000, find the area on the map which would represent an... (answered by swincher4391)
the scale of a detailed map is 1:2000. find the actual area, in square metres, for each... (answered by rfer)
On a map of scale 1:20000 the area of a forest is 50cm2. On another map the area of the... (answered by CubeyThePenguin)
Map of Oxfordshire has a scale of 1:25000. If the distance from Islip to Beckley is 18 cm (answered by solver91311)
A map-maker wants to represent an area of roughly using the scale . What area will the (answered by jim_thompson5910)
The scale of a map is 1:20,000.Calculate the area, in square centimeters, on the map of a (answered by Boreal)
On a map with a scale of 1cm:100m, if the area of a field is 180 m2 on the map, what is... (answered by Theo)
The scale of a map is 1:20 000. Find the area on the map which represents 124km squared. (answered by Theo)