Geology Question MATH. Please Help.?

Suppose you are given three maps, A, B, C (each 17.5 inches long by 13.5 inches wide). Map A has a scale of 62,500: map B a scale of 125,000; and map C a scale of 250,000.





How much area is shown on C compared to that shown on B?





How much area is shown on C compared to that shown on A/?

Geology Question MATH. Please Help.?
the larger the scale of the map (1:62500, 1:125,000, 1:250,000), the more area that is portrayed on the map.





Distances on a map with a scale of 1:4 are twice as long as distances on a map with a scale of 1:2.


Since 1:250,000 (C) is twice the scale of 1:125,000 (B), then one inch on C is twice the distance as one inch on B.





Since Area is equal to length times width, and the maps are physically the same size, C shows an area that is twice as long and twice as wide as B or 2x2 times as much. So C shows 4 times the area that B does.





NOW, it's your turn. Divide C's scale by A's scale to find out how much larger C's scale is than A's. Then do what I did above to come up with the C to A area ratio. If you email me, I'll verify your answer.
Reply:I CRY FOUL!





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Reply:Firstly area must be expressed in areal units, which are usually distance units squared, in this case, sq in.





Follow these steps:





(1) Find the area of the map in map units (same for all 3 maps)





17.5 sq in x 13.5 sq in = 236.25 sq in





(2) multiply it by the scale for each map





MAP A


x = map area x (ground / map)^2


x = 236.25 in sq x (62500 / 1) ^ 2


x = 236.26 in sq x (3906250000)


x = 922,851,562,500 sq in








(3) Convert to a larger measurement of area, such as square miles.





x = 922,851,562,500 sq in / 4,014,489,600 sq in/sq mi


x = 229.880173 sq mi








(4) Compare the maps to find the difference. You can do this by dividing them and finding a ratio or comparing absolute area.





HINT FOR (4): 62500 is 2x smaller than 125000


125000 is 2x smaller than 250000








I'll let you do Map B and Map C, but just follow that, and substitute the scale in and you will be good to go.





Hope that helps.