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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

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