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Solving Scale Problems. The solution will gradually “build” for each problem. Some unit conversions. 1 m = 100 cm = 1000 mm 1 km = 1000 m 1 foot = 12 inches (1’ = 12”) 1 mile = 63,360 inches 1 hectare (ha) = 10,000m 2.

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solving scale problems

Solving Scale Problems

The solution will gradually “build” for each problem

some unit conversions
Some unit conversions
  • 1 m = 100 cm = 1000 mm
  • 1 km = 1000 m
  • 1 foot = 12 inches (1’ = 12”)
  • 1 mile = 63,360 inches
  • 1 hectare (ha) = 10,000m2
slide3
The real world distance between 2 features is 1600m and the map distance is 8 cm.What is the map scale ?
  • Scale = 1 / xxxxx = map dist / real world distance
  • If we know 3 of the figures, then we solve for the unknown by cross-multiply & then divide
  • What are we solving for?
    • Map scale is unknown
    • 1 / xxx = map dist. / real world (RW) dist
  • What do we know?:
    • Map dist = 8 cm
    • RW distance is 1,600 m = 160,000 cm
  • 1 / xxx = 8 cm / 160,000 cm
    • xxx = (1*160,000 cm)/8 cm
    • xxx = 20,000
    • Scale is 1 : 20,000
the distance between 2 features on a 1 10 000 map is 5 cm what is the real world distance
The distance between 2 features on a 1:10,000 map is 5 cm. What is the real world distance?
  • Scale = 1 / xxxx = map dist / real world distance
  • If we know 3 of the figures, then we solve for the unknown by cross-multiply & then divide
  • What are we solving for?
    • Real world (RW) distance
    • 1 /xxxx = map dist / RW dist
  • What do we know?:
    • Scale of map (1/xxxx) is 1 / 10,000
    • Map dist = 5 cm
  • 1 / 10,000 = 5 cm / RW dist. cm
    • RW dist (cm) = (5*10,000 cm)/1
    • RW dist cm = 50,000 cm
    • In metres, RW dist = 500 m
what is the length in cm of one km on a 1 25 000 map
What is the length in cm of one km on a 1:25,000 map?
  • Scale = 1 / xxxxx = map dist / real world distance
  • If we know 3 of the figures, then we solve for the unknown by cross-multiply & then divide
  • What are we solving for?
    • Length on map (in cm)
    • 1 / x = map dist. / real world (RW) dist
  • What do we know?:
    • Scale of map (1/x) is 1 / 25,000
    • 1 km RW dist (1 km = 1,000 m = 100,000 cm)
  • 1 / 25,000 = map dist cm / 100,000 cm
    • Map dist (cm) = (1*100,000 cm)/25,000
    • Map dist = 4 cm
you have a photo with a scale expressed as 1 mile what is the scale as a representative fraction
You have a photo with a scale expressed as 1” = ¼ mile. What is the scale as a representative fraction?
  • This is really a unit conversion question
  • Scale = 1 / xxx = map / RW
  • Scale of photo is 1” = ¼ mile
  • If you convert top and bottom values to the same units, then you have a representative fraction (since the units will cancel out)
  • So the question really is … how many inches in ¼ mile?
  • 1 mile = 63,360 inches
  • ¼ mile = 63,360 inches / 4 = 15,840 inches
  • Scale is 1 : 15,840 (NO need to show units anymore)
slide7
A map scale is 1 cm = 750 m and a photo covers a portion of the map area.  The distance between two road intersections measures 9.8 cm on the photo and 5.0 cm on the map.  Determine the scale of the photo.
  • Photo scale = 1/xxx = photo/RW
  • We know
    • photo measure of 9.8 cm
  • If we had the RW distance we could determine the photo scale.
  • Can we find RW distance?
    • Yes, as we have map scale and a map measure
  • So first we find RW distance from map, then use it to solve for photo scale
  • Map scale is
    • 1 cm = 750 m, or
    • 1 cm = 75,000 cm, or
    • 1 : 75,000
  • RW distance is
    • RW = 5.0 cm * 75,000
    • RW = 375,000 cm
slide8
A map scale is 1 cm = 750 m and a photo covers a portion of the map area.  The distance between two road intersections measures 9.8 cm on the photo and 5.0 cm on the map.  Determine the scale of the photo.
  • From last slide
  • Photo scale is …
  • RW distance (from map measures) is
    • RW = 5.0 cm * 75,000
    • RW = 375,000 cm
  • Realize that RW distance is the same no matter if we calculated from a map or a photo – the RW distance is the same
  • Now we can solve for photo scale (xxxx)
    • xxxx = (1 * 375,000cm) / 9.8 cm
    • xxxx = 38,265
    • Scale is 1 : 38,265
solve for area
Solve for Area
  • The unit we will use for an area measure is the hectare (ha)
  • 1 ha = 10,000 m2
  • You can visualize this as a large square that measures 100m on each side.
how many hectares are covered by a standard air photo at a scale of 1 20 000
How many hectares are covered by a standard air photo at a scale of 1:20,000
  • First remember that an air photo measures 9” by 9”
  • We want to know what ground area is covered in the photo.
  • First, since we will be solving for a metric area measure (ha), it is best to first convert 9” to cm
    • Photo edge = 9 in
    • = 9 in * 2.54 cm/in
    • = 22.86 cm
  • Second, we find the RW distance in metres
    • RW = (20,000*22.86cm) / 1
    • RW = 457200 cm = 4572 m
  • Third, we find area (L * W)
    • Area = 4572m * 4572m
    • Area = 20903184m2
    • Area = 2090 ha
how many hectares are covered by a standard air photo at a scale of 1 mile
How many hectares are covered by a standard air photo at a scale of 1” = ¼ mile
  • The photo scale 1” = ¼ mi. needs to be converted to a representative fraction
    • Solve by converting ¼ mi to inches
    • 63,360 in/mi / 4 = 15,840”
  • Next, convert the photo edge (9”) to metric (cm)
    • Since we will be solving for a metric measure (ha), it is best to first convert 9” to cm
    • Photo edge = 9 in
    • = 9 in * 2.54 cm/in
    • = 22.86 cm
  • Now we find the RW distance of the photo edge
    • RW cm = (22.86 cm*15840)/1
    • RW = 362,102 cm = 3621 m
  • Last we calculate area, in m2, then convert to ha
    • Area = 3621 m * 3621 m = 13,111,641 m2
    • Area = 13,111,641 m2 / 10,000 = 1,311 ha
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