The scale of a map is 1:1000. What is the area, in cm2, on the map of a lake of area 5000 cm2?
area grows as the square of the scale, so the area are in the ratio
1:1000^2
so the map has area
5000/1000^2 = 5/1000 = 1/200 = 0.005 cm^2
To find the area of the lake on the map, we can use the scale of the map. The scale of 1:1000 means that every 1 unit on the map represents 1000 units in reality.
The lake has an area of 5000 cm² in reality. Since the scale is 1:1000, we need to divide the real area by 1000 to find the corresponding area on the map.
5000 cm² ÷ 1000 = 5 cm²
Therefore, the area on the map of the lake is 5 cm².
To find the area of a lake on a map, given its real-world area and the scale of the map, you need to set up a proportion.
The scale of the map is given as 1:1000, which means that 1 unit on the map represents 1000 units in the real world.
Let's assign variables:
Let A represent the area on the map.
Let L represent the real-world area of the lake.
The proportion we can set up is:
1 cm^2 (map area) / 1000 cm^2 (real-world area) = A cm^2 / L cm^2
Now we can solve for A (the area on the map):
A cm^2 = (1 cm^2 / 1000 cm^2) * L cm^2
Substituting the given value for the real-world area of the lake:
A cm^2 = (1 cm^2 / 1000 cm^2) * 5000 cm^2
Simplifying the equation:
A cm^2 = (1/1000) * 5000 cm^2
A cm^2 = 5 cm^2
Therefore, the area on the map of a lake that has a real-world area of 5000 cm^2 is 5 cm^2.