4.03 Scales, maps and ratios
Convert the following descriptions to a scale ratio:
3 \text{ cm} represents an actual distance of 9 \text{ m}.
20\text{ cm} represents an actual distance of 16\text{ km}.
8\text{ mm} represents an actual distance of 40\text{ m}.
60 \text{ mm} represents an actual distance of 5400 \text{ m}.
5 \text{ cm} represents an actual distance of 30 \text{ km}.
98 \text{ mm} represents an actual distance of 9.8 \text{ km}.
6\text{ in} represents an actual distance of 42\text{ ft}.
36\text{ in} inches represents an actual distance of 15\text{ yd}.
The scale of the map is 1:2000 and two points are drawn 19 \text{ cm} apart on the map. Find the actual distance between the points in meters.
Find the distance between two lakes drawn on a map if the scale on the map is 1\text{ cm}: 3 \text{ km}, and the actual distance between the lakes is 147\text{ km}.
On a map, 7\text{ cm} represents a distance of 63\text{ km}.
Write the scale as a ratio in simplified form.
Find the actual distance, in kilometers, represented on the map by 5\text{ cm}.
Find the distance on the map, in centimeters, that represents an actual distance of 54\text{ km}.
The scale of the map is 1:300 and two points are drawn 21 \text{ in} apart on the map. Find the actual distance between the points in yards.
The scale of the map is 1:25\,000 and two points are drawn 16 \text{ in} apart on the map. Find the actual distance between the points in yards, correct to two decimal places.
The scale of the map is 1:100 and two points are drawn 17 \text{ in} apart on the map. Find the actual distance between the points in feet, correct to two decimal places.
The scale on a map is 1:400\,000. How far apart on the map should two train stations be drawn if the actual distance between the stations is 100 \text{ km}? Express your answer in centimeters.
A swimming pool of length 40\text{ m} and width 20\text{ m} is to be represented on a scale drawing with a scale of 1:2000. Find the scale dimensions of the pool in centimeters.
Find the length in centimeters.
Find the width in centimeters.
Bianca is looking over a map of her local area and notices that the scale of the map is given as 1:100 in the map legend.
Find the actual distance (in centimeters) between two points which are drawn 12 \text{ cm} apart on that map.
Find the distance between the two points in meters.
The scale on a map is 1:500\,000. If 1 \text{ mi}=63\,360\text{ in}, how far apart on the map should two train stations be drawn if the actual distance between the stations is 100 \text{ mi}? Express your answer in inches correct to two decimal places.