Geography 2275: Cartography: Map Scale Exercise 1) If two cities are 6 inches ap

Question

Geography 2275: Cartography: Map Scale Exercise

1) If two cities are 6 inches apart on a map & you know they are 75 miles from each other, what is the scale of the map?
In English verbal?


Representative Fraction/Ratio?


Metric Verbal? ____________________________

The scale on a given map is 1 inch: 40 miles.


How many inches would a bar scale be that represented 100 miles? _________________


Representative Fraction? _________________________


Metric Verbal? __________________________


Change the following Representative Fractions & Verbal scale types.
12 inches: 1 mile RF_________________ 1 cm: _________________km
3 inches: 23 miles RF_________________ 1 cm: _________________km
3.2 cm: 12.3 km RF_________________ 1 in: _________________mi




Geography 2275: Cartography: Map Scale Exercise

1) If two cities are 6 inches apart on a map & you know they are 75 miles from each other, what is the scale of the map?
In English verbal?


Representative Fraction/Ratio?


Metric Verbal? ____________________________

The scale on a given map is 1 inch: 40 miles.


How many inches would a bar scale be that represented 100 miles? _________________


Representative Fraction? _________________________


Metric Verbal? __________________________


Change the following Representative Fractions & Verbal scale types.
12 inches: 1 mile RF_________________ 1 cm: _________________km
3 inches: 23 miles RF_________________ 1 cm: _________________km
3.2 cm: 12.3 km RF_________________ 1 in: _________________mi




Geography 2275: Cartography: Map Scale Exercise

1) If two cities are 6 inches apart on a map & you know they are 75 miles from each other, what is the scale of the map?
In English verbal?


Representative Fraction/Ratio?


Metric Verbal? ____________________________

The scale on a given map is 1 inch: 40 miles.


How many inches would a bar scale be that represented 100 miles? _________________


Representative Fraction? _________________________


Metric Verbal? __________________________


Change the following Representative Fractions & Verbal scale types.
12 inches: 1 mile RF_________________ 1 cm: _________________km
3 inches: 23 miles RF_________________ 1 cm: _________________km
3.2 cm: 12.3 km RF_________________ 1 in: _________________mi

Explanation / Answer

a) If two cities are 6 inches apart on a map & you know they are 75 miles from each other.

Scale conversion:

75 miles/ 6 inches = 12.5 miles/ 1 inch = 792000 inches/ inch

(1 mile = 63360 inches)

In English verbal: 1 inch represents 12.5 miles

Representative Fraction/Ratio: 1 inch : 792000 inches

Metric verbal: 1 inch : 12.5 miles

b) The scale on a given map is 1 inch: 40 miles

How many inches would a bar scale be that represented 100 miles?

So the scale in english verbal means, 1 inch equals 40 miles

x inches equals 100 miles

1/x = 40/100 => x =100/40 = 2.5

Thus 100 miles equals 2.5 inches on map.

Representative Fraction: 1 inch : 40 miles = 1 inch: 40*63360 inches = 1 inch: 2534400 inches

Metric verbal: 1 inch : 40 miles

c) Change the following Representative Fractions & Verbal scale types

12 inches: 1 mile

(inches to cms and miles to kms)

1 inch = 2.54 cm => 12 inches = 30.48 cms

1mile = 1.61 km (approximately)

12 inch/1 mile = 30.48 cm/1.61 km = 18.93 cm/1km

thus

12 inches: 1 mile RF = 30.48 cm: 1.61 km = 18.93 cm : 1km

Similarly

3 inches: 23 miles RF= 7.62 cm: 37.015km = 1 cm : 4.86 km

3.2 cm: 12.3 km RF= 1.26 in:7.64 mi = 1 in : 6.07 miles

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