Solutuins: Scale

Problem (1)

Convert the following scale equivalencies to ratios.

(a) 500 ft x (12 in / 1 ft) = 6000
(b) 100 m x (1000 mm / 1 m)=100,000
(c) 6.25 mi x (5280 ft / 1 mi) x (12 in / 1 ft) = 396,000
(d) 1'-0" x (12"/1') = 12"
      multiply both sides by 8/3: 12"x (8/3) = 32

Problem (2)

The distance between two property corners is 388.64 feet. What would the line's length be, in inches, on a 1:600 map?
L = 388.64 ft x (1/600) x (12 in / 1 ft) = 7.7728 in = 7.77 in

Problem (3)

What is the area, in acres, of a field that is 6.59 in x 3.88 in on a 1:1000 map?
6.59 in x (1000/1) x (1 ft / 12 in) = 549.16667 ft
3.88 in x (1000/1) x (1 ft / 12 in) = 323.33333 ft
Area = 549.16667 ft x 323.33333 ft x (1 ac / 43,560 ft²) = 4.07630 ac = 4.08 ac

Problem (4)

A 1 in = 600 ft paper map has been enlarged 2.5 times. On the enlarged map, a line measures 3.75 inches long on. What is the ground length of the line?
Enlarged scale is 600/2.5 >> 1 in = 240 ft
L = 3.75 ft x 240 ft / 1 in) = 900. ft

Problem (5)

A surveyor has a map with an unknown scale. She identifies two distinct points on the map, a fire hydrant and center line intersection, which she can also find in the field. On the map, the distance between the two points is 7.85 inches. She measures 391.5 ft between the two points using a total station. What is the scale of the map expressed as an equivalency? 1 in = __________ ft
(7.85 in / 391.5 ft) = (1 in / X)
>> X = 1 in x (391.5 ft / 7.85 in) = 49.8726 ft
>> 1 in / 50 ft

Problem (6)

To fit it in a report, a student reduces a 1:10,000 map by 55%. What is the scale of the reduced map? Express as a ratio.
The map is 45% of its original size; its scale has gotten smaller.
(1/10,000) x 0.45 = 0.45/10,000
0.45/10,000 = 1/X >> X = 10,000/0,45 = 22,222
Scale is 1:22,000

Problem (7)

An area that is 400 ft wide by 710 feet long will be surveyed and mapped. What is the maximum engineering scale at which the map can be plotted on an 11" x 17" sheet? Express as an equivalence: 1 in = __________ ft
Orient short side of paper to short side of area.
Scale width = 11 in / 400 ft >> 1 in = 36.4 ft   next engr scale is 1 in = 40 ft
Scale length = 17 in / 710 ft >> 1 in = 41.8 ft    next engr scale is 1 in = 50 ft
Must use smaller of the two scales: 1 in = 50 ft.

Problem (8)

For planning purposes, a client needs a topographic map at a scale of 1 inch = 30 feet. The area is approximately 450 ft x 650 ft. The map must have a margin of one inch on all four sides. What smallest ANSI sheet size can be used for the map?
Standard ANSI sheet sizes in inches are A:8.5x11, B:11x17, C:17x22, D: 22x34, E:34x44
Width: 450 ft x (1 in / 30 ft) = 15 in
Add 2 in margins: 17 in
Length: 650 ft x (1 in / 30 ft) = 21.7 in
Add 2 in margins: 23.17 in
Just too big to fit on C size sheet.
Use D size, 22 in x34 in, sheet.