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Question 1038498: A map is drawn to a scale of 1 : 25000
(a) The distance between two towns on the map is 15cm. Find the actual distance, in kilometers, between the two towns.
(b) A lake has an actual area of 3.5km^2. Find the area, in square centimeters, of the lake on the map.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the scale of the map is 1:25000
this means that 1 centimeters on the map is equal to 25000 centimeters in the real world.
the distance between 2 towns on the map is 15 centimeters.
this means that the distance between the two towns in the real world is 15 * 25000 = 375000 centimeters.
since 1 kilometer is equal to 100,000 centimeters, this means that the distance between the 2 towns is 375,000 / 100,000 = 3.75 kilometers.
that's the answer to the first question.
the area of the lake in the real world is 3.5 square kilometers.
1 square kilometer is equal to 1 kilometers squared.
since 1 kilometer is equal to 100,000 centimeters, then 1 square kilometer is equal to 100,000^2 centimeters which is equal to 1 * 10^10 square centimeters.
3.5 square kilometers on the map is therefore equal to 3.5 * 10^10 square centimeters.
1 centimeter on the map is equal to 25000 centimeters in the real world.
1 square centimeter on the map is equal to 25000^2 centimeters in the real world which is equal to 625 * 10^6 square centimeters in the real world.
take 3.5 * 10^10 square centimeters in the real world and divide it by 625 * 10^6 square centimeters and you get .0056 * 10^4 square centimeters which is equal to 56 square centimeters on the map.
the answer to your second question is that the area of the lake on the map is equal to 56 square centimeters.
you could also have done some conversions up front that may have helped you to avoid dealing with hundreds of thousands of centimeters.
for example:
1 centimeter on the map is equal to 25000 centimeters in the real world.
25000 centimeters in the real world is equal to .25 kilometers in the real world.
therefore, 1 centimeter on the map is equal to .25 kilometers in the real world.
the distance between the towns is 15 centimeters which is equal to 15 * .25 = 3.75 kilometers in the real world.
the area on the lake in the real world is 3.5 square kilometers.
since 1 centimeter on the map is equal to .25 kilometers in the real world, then 1 kilometer in the real world is equal to 4 centimeters on the map.
1 square kilometer in the real world is therefore equal to 4^2 = 16 square centimeters on the map.
3.5 square kilometers in the real world is therefore equal to 3.5 * 16 square centimeters on the map which is equal to 56 square centimeters on the map.
that's the answer to the second question.
it's a tossup as to which way is easier.
try one way.
if you get all botched up, then try another.
i tried both.
i'm not sure which was easier, although i did both methods and felt better when they both agreed to the same solution.
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