Solving Scale Problems

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# Solving Scale Problems - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Solving Scale Problems' - nuala

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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) = 10,000m2
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?
• 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?
• 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” = 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)
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
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
• 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
• 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” = 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