A distance of 12km is represented by a length of 4cm on a map.Given that the scale of the map is 1:n,find the a)value of n b)actual area in hectares of a field on the map with an area of 32cm^2
Am not really getting the last part
4cm/12km=1cm/nkm or
n=3km
area: 1cm^2=9km^2=900 hectacres
scale:
4 cm : 12 km
4 cm : 12000 m
4 cm : 1200000 cm
1 : 300,000 <----- scale without units
for that scale:
1 cm : 3,000 m
1 cm^2 : 9,000,000 m^2
32 cm^2 : 288,000,000 m^2
we know 1 hectare = 100 m by 100 m or 10,000 m^2
so 288,000,000 m^2 = 288,000,000/10,000 hectares
= 28,800 hectares
To understand maath
To find the value of n, we can set up a proportion using the given information:
12 km --> 4 cm
Since the length on the map is in centimeters while the actual distance is in kilometers, we need to convert the length to the same unit.
1 km = 1000 m
1 m = 100 cm
So, 12 km = 12,000 m = 12,000 × 100 cm = 1,200,000 cm
Now we can set up our proportion:
12,000,000 cm / 12 km = 4 cm / 1
Simplifying the proportion gives us:
12,000,000 / 12 = 4
Solving for n:
n = 12,000,000 / 12 = 1,000,000
Therefore, the value of n is 1,000,000.
To find the actual area in hectares of a field on the map with an area of 32 cm^2, we need to take into account the scale of the map.
Given that 1 hectare is equal to 10,000 square meters, we can convert the map's area to square meters first:
32 cm^2 × (1 m / 100 cm)^2 = 0.0032 m^2
Next, we can convert the area to hectares:
0.0032 m^2 × (1 hectare / 10,000 m^2) = 0.00000032 hectares
Therefore, the actual area in hectares of the field on the map with an area of 32 cm^2 is 0.00000032 hectares.