On a map of scale 1:10,000 the area of a lake is 12cmsquare .what is the area of the actual lake?
area is proportional to the scale^2. So,
12cm^2 * (10^4)^2 = 12*10^8 cm^2
since 1m^2 = 10^4 cm^2, that means the area of the real lake is
12*10^4 m^2 = 12 ha
1:10 000
(1)^2 : (10 000)^2
12cm2 : ?
12 X 100 000 000
1200 000 000cm2
1m2 = (100)^2cm2
1200 000 000/10 000
120 000m2
10 000m2 = 1 Ha
120 000/10 000
12Ha
To find the area of the actual lake, given a scale of 1:10,000 and an area on the map of 12 cm², you can use the concept of scale factor.
The scale factor is the ratio of the length on the map to the actual length. Since it is a 2-dimensional problem, the scale factor for area is the ratio of the area on the map to the actual area.
In this case, the scale factor for the area would be:
Scale factor = Actual Area / Area on the map
Given that the area on the map is 12 cm², and the scale is 1:10,000, we can calculate the scale factor as follows:
Scale factor = Actual Area / Area on the map
Scale factor = Actual Area / 12 cm²
Scale factor = 1 / 10,000
To find the actual area of the lake, we multiply the scale factor by the area on the map:
Actual Area = Area on the map * Scale factor
Actual Area = 12 cm² * (1 / 10,000)
Calculating this:
Actual Area = 12 cm² * 0.0001
Actual Area = 0.0012 cm²
Therefore, the actual area of the lake is 0.0012 cm².
To find the area of the actual lake, we need to use the given scale. In this case, the scale is 1:10,000, which means that 1 unit on the map represents 10,000 units in real life.
First, let's determine the measurement of the lake on the map. We know that the area on the map is 12 cm². Since the area is calculated by multiplying the length with the width, we can assume that the length and width are 4 cm each (since 4 cm × 4 cm = 16 cm², which is closest to our given area of 12 cm²).
Now, we can calculate the actual area of the lake using the scale. Since 1 cm on the map represents 10,000 cm in real life, we will need to multiply the length and width by 10,000 to get the actual area.
Length on the map: 4 cm
Length in real life: 4 cm × 10,000 = 40,000 cm
Width on the map: 4 cm
Width in real life: 4 cm × 10,000 = 40,000 cm
Actual area of the lake: 40,000 cm × 40,000 cm = 1,600,000,000 cm²
Therefore, the area of the actual lake is 1,600,000,000 cm².