Find the areal scale for the following
1cm to 6km
(1cm:6km)^2 = 1 cm^2 : 36 km^2
To find the areal scale, we need to determine the ratio between the measurements on the map and the corresponding measurements on the ground.
Given that 1 cm on the map represents 6 km on the ground, we can set up a conversion ratio:
1 cm on map / 6 km on ground
To simplify this ratio, we can convert 6 km to cm by multiplying it by 100, since there are 100 cm in 1 meter:
1 cm on map / 6,000 cm on ground
Now, we have the areal scale:
1 : 6,000
This means that 1 cm on the map represents 6,000 cm (or 6 km) on the ground.
To find the areal scale, we need to determine the relationship between the measurements on the map and the actual measurements on the ground.
In this case, we are given that 1 centimeter on the map represents 6 kilometers on the ground.
To find the areal scale, we can use the formula:
Areal Scale = Map Distance / Ground Distance
In this case, the map distance is 1 centimeter and the ground distance is 6 kilometers.
Areal Scale = 1 cm / 6 km
To make the units consistent, we need to convert 6 kilometers to centimeters.
1 kilometer = 100,000 centimeters
Therefore, 6 kilometers = 6 * 100,000 centimeters = 600,000 centimeters.
Now we can substitute the values into the formula:
Areal Scale = 1 cm / 600,000 cm
Simplifying the fraction, we get:
Areal Scale = 1/600,000
Therefore, the areal scale for 1 cm to 6 km is 1/600,000.