Question

d. map scales
the scale of a map shows the relationship between the length of a line on that map and the distance represented by that line on the ground. this relationship can be expressed by a fractional scale, which is either a ratio or a representative fraction (rf), designating the length of the line on the map equal to 1. for example, a scale of 1:24,000 (or 1/24,000 rf) is taken to mean that the length of a measurement along the edge of an english or metric rule represents 24,000 times that length in actual distance on earths surface. to illustrate...
q2.10 given a scale of 1:24,000: (a) what is the ground - distance in feet represented by three inches on the map? (b) what is the ground distance in meters represented by 5 cm on the map? (c) how about the ground distance in kilometers represented by 5 cm on the map?
hint: multiples of units of measures - and their conversions to other systems of measures - appear on pages i and ii at the front of this manual.
a relatively large fraction, for example, 1:24,000, is called a large - scale map; a relatively small fraction, for example, 1:250,000, is called a small - scale map. a large - scale map represents a smaller land area in greater detail than does a small - scale map on a sheet of paper of the same size.
another kind of scale is the graphic scale, the application of which is demonstrated in figure 2.8 in two simple steps.
a graphic scale has two advantages over a fractional scale.

• first, a graphic scale can be applied visually, rather than through mathematical computation.
• second, suppose you have a map on which both fractional and graphic scales are indicated. you would like an enlargement of your map, so you take it to a copy center and ask to have it enlarged by whatever percent you choose.

q2.11 what happens to the usefulness of (a) the fractional scale, and (b) the graphic scale, as you enlarge your map?
step 1
step 2
figure 2.8 a simple way in which to measure the ground distance between two points on a map using a graphic scale:
step 1: place two marks labeled a and b on a sheet of scrap paper, indicating the separation between two points on the map.
step 2: bring the paper with the two marks to the graphic scale on the map and read the ground distance directly: 1,600 feet.

Explanation:

Step1: Recall map - scale formula

The scale 1:24000 means 1 unit on the map represents 24000 units on the ground.

Step2: Solve part (A)

We know 1 inch on the map represents 24000 inches on the ground. For 3 inches on the map, the ground - distance in inches is $3\times24000 = 72000$ inches. Since 1 foot = 12 inches, the ground - distance in feet is $\frac{72000}{12}=6000$ feet.

Step3: Solve part (B)

The scale is 1:24000. 1 cm on the map represents 24000 cm on the ground. For 5 cm on the map, the ground - distance in cm is $5\times24000 = 120000$ cm. Since 1 m = 100 cm, the ground - distance in meters is $\frac{120000}{100}=1200$ m.

Step4: Solve part (C)

From part (B), the ground - distance for 5 cm on the map is 120000 cm. Since 1 km = 100000 cm, the ground - distance in kilometers is $\frac{120000}{100000}=1.2$ km.

Step5: Analyze part (A) of Q2.11

When the map is enlarged, the fractional scale remains the same because the ratio of map distance to ground distance is a fixed property of the map and does not change with the size of the map. So its usefulness remains the same as it still represents the correct ratio of distances.

Step6: Analyze part (B) of Q2.11

When the map is enlarged, the graphic scale becomes inaccurate. The distances marked on the graphic scale no longer correspond to the correct ground distances on the enlarged map. So its usefulness decreases.

Answer:

(A) 6000 feet
(B) 1200 m
(C) 1.2 km
Q2.11 (A) The usefulness remains the same.
Q2.11 (B) The usefulness decreases.