the scale of a mao is 1:6000000
a) the distance between 2 towns on the map is 8.7cm. what is the actual distance?
1 cm on the map repersents cm of the actual distance
the actual distance between the two towns is
x cm= cm= km
b) the distance between 2 other towns is 248km. What is the distance on the map?
1cm ----> 6 000 000 cm
8.7 cm --->52,200,000 cm = 522 km
we could use this result and a proportion to find the second part
8.7/522 = x/248
522x = 2157.6
x = 62/15 or appr 4.13 cm
a) To find the actual distance between the two towns, we need to set up a proportion using the scale provided.
The scale is 1:6000000, which means 1 cm on the map represents 6000000 cm in actual distance.
Let's set up the proportion:
1 cm on the map / 6000000 cm = 8.7 cm on the map / x cm
By cross-multiplying and solving for x, we can find the actual distance:
x = (8.7 cm * 6000000 cm) / 1 cm
x = 52200000 cm
To convert cm to km, we divide by 100000:
x = 52200000 cm / 100000 = 522 km
Therefore, the actual distance between the two towns is 522 km.
b) To find the distance on the map between the two other towns, we can use the same scale:
The scale is 1:6000000, which means 1 cm on the map represents 6000000 cm in actual distance.
Let's set up a proportion:
1 cm on the map / 6000000 cm = x cm on the map / 248 km
By cross-multiplying and solving for x, we can find the distance on the map:
x = (1 cm * 248 km) / 6000000 cm
x = 0.00004133333 km (approximately)
To convert km to cm, we multiply by 100000:
x = 0.00004133333 km * 100000 cm
x = 4.133333 cm (approximately)
Therefore, the distance on the map between the two other towns is approximately 4.133333 cm.
To find the actual distance between two towns on a map, knowing the scale, we can use the following steps:
a) Given: Scale of the map is 1:6000000
Distance on the map = 8.7 cm
1. Determine the ratio of map distance to actual distance:
The scale 1:6000000 means that 1 cm on the map represents 6000000 cm or 60000 meters in real life. So we have the ratio:
1 cm on the map represents 60000 meters (or 6000000 cm) of the actual distance.
2. Use the ratio to find the actual distance:
Cross-multiplication can be used to solve proportions.
1 cm on the map represents 6000000 cm of the actual distance
Therefore, 8.7 cm on the map represents x cm of the actual distance.
Setting up a proportion:
1 cm / 6000000 cm = 8.7 cm / x cm
Cross-multiplying:
1 * x = 6000000 * 8.7
x = 6000000 * 8.7
Calculating the actual distance:
x = 52200000 cm
To convert cm to km, divide by 100,000:
x = 52200000 cm / 100000 = 522 km
Therefore, the actual distance between the two towns is 522 km.
b) Given: Actual distance between two towns is 248 km
1. Determine the ratio of actual distance to map distance:
We need to find out how many centimeters on the map represent 248 km in real life.
Since 1 cm on the map represents 60000 meters (or 6000000 cm) in real life, we set up the proportion:
1 cm / 6000000 cm = x cm / 24800000 cm
Cross-multiplying:
6000000 * x = 1 * 24800000
x = (1 * 24800000) / 6000000
Calculating the distance on the map:
x = 24800000 / 6000000
Simplifying the fraction:
x = 4.133333333333333 cm
Therefore, the distance between the two towns on the map is approximately 4.13 cm.