Question

1. a map with a 1:10,000 scale means that ____ unit on the map is equal to ____ units on the ground.
2. calculate the contour interval for the maps below:

Explanation:

Step1: Identify known contours

In the first contour map, we have contour lines labeled 20, 40, 60. Let's take two adjacent labeled contours, say 20 and 40 (or 40 and 60).

Step2: Calculate the difference

The difference between 40 and 20 is \( 40 - 20 = 20 \), and between 60 and 40 is \( 60 - 40 = 20 \). Now, check the number of intervals between them. From 20 to 40, there is 1 interval (since they are adjacent labeled contours? Wait, no, looking at the map, between 20 and 40, how many contour lines? Wait, the labels are 20, then next labeled is 40? Wait, maybe the first map: let's see, the outermost is 60, then 40, then 20? Wait, no, the labels are 20, 40, 60. Wait, maybe the interval between 20 and 40: let's count the number of contour lines between them. Wait, maybe the contour interval is the difference between two adjacent contour lines. Let's take 60 and 40: \( 60 - 40 = 20 \), and 40 - 20 = 20. Wait, but maybe the number of lines between? Wait, no, contour interval is the vertical difference between adjacent contour lines. So if we have 20, then next is, say, 30? No, the labels are 20, 40, 60. Wait, maybe the distance between 20 and 40 is two intervals? Wait, no, maybe I misread. Wait, the first map: the outermost contour is 60, then inside is 40, then 20. Wait, no, the labels are 20, 40, 60. Wait, maybe the contour interval is \( \frac{60 - 20}{2} = 20 \)? No, wait, between 20 and 40, how many contour lines? Let's see, the map has 20, then a line, then 40? No, the labels are 20, 40, 60. Wait, maybe the contour interval is 20? Wait, no, let's take 60 - 40 = 20, 40 - 20 = 20. So the contour interval is 20? Wait, no, maybe the first map: the outermost is 60, then next is 40 (difference 20), then next is 20 (difference 20). So the contour interval is 20? Wait, no, maybe I made a mistake. Wait, let's check the second map: the outermost is 140, and the innermost is, say, 200? Wait, no, the second map's label is 140. Wait, maybe the first map: contour interval is 20? Wait, no, let's do it properly. Contour interval (CI) = (Highest contour - Lowest contour) / Number of intervals. But in the first map, labeled contours are 20, 40, 60. So from 20 to 60, the difference is 40, and the number of intervals between them: from 20 to 40 is 1 interval, 40 to 60 is another. Wait, no, the number of contour lines between 20 and 60: if 20, then 30, 40, 50, 60? No, the labels are 20, 40, 60. So maybe the contour interval is 20, because 60 - 40 = 20, 40 - 20 = 20. So the contour interval is 20. Wait, but let's confirm. For the first map:

Take two adjacent labeled contour lines, say 40 and 60. The difference is \( 60 - 40 = 20 \). Since they are adjacent (how many contour lines between them? If there's one contour line between 40 and 60, then the interval would be 10, but no, the labels are 20, 40, 60. Wait, maybe the first map has contour lines at 20, 30, 40, 50, 60? But the labels are 20, 40, 60. So the labeled contours are every other line. So the actual contour interval is \( \frac{40 - 20}{1} = 20 \)? No, that can't be. Wait, maybe I'm overcomplicating. Let's take the first map: the outermost is 60, then inside is 40 (difference 20), then inside is 20 (difference 20). So the contour interval is 20. Wait, but maybe the second map: the outermost is 140, and the innermost is, say, 200? Wait, no, the second map's label is 140. Wait, maybe the first map's contour interval is 20, and the second map: let's see, the outermost is 140, and the innermost is, say, 200? Wait, no, maybe the second map's contour interval: let's assume the first map's is 20, but maybe the question is about the first map? Wait, the problem says "Calculate the contour interval for the maps below." Let's focus on the first map (top one) with labels 20, 40, 60.

So, contour interval (CI) is the difference in elevation between adjacent contour lines. Let's take two adjacent labeled contour lines, e.g., 40 and 60. The elevation difference is \( 60 - 40 = 20 \). Now, how many contour lines are between them? If there's one contour line between 40 and 60, then the interval would be \( \frac{20}{1} = 20 \)? Wait, no, if 40 and 60 are two contour lines apart (with one line in between), then the interval is \( \frac{60 - 40}{1} = 20 \). Wait, maybe the contour lines are 20, 30, 40, 50, 60? But the labels are 20, 40, 60. So the labeled contours are every 20 units, with the contour interval being 10? No, that doesn't make sense. Wait, maybe the first map: the outermost is 60, then next is 40 (difference 20), then next is 20 (difference 20). So the contour interval is 20. Wait, but let's check the formula: CI = (Higher elevation - Lower elevation) / Number of intervals between them. For 60 and 20: difference is 40, number of intervals between them: from 20 to 60, how many contour lines? If 20, then 30, 40, 50, 60: that's 4 intervals (from 20 to 30, 30 to 40, 40 to 50, 50 to 60). But the labels are 20, 40, 60. So the labeled contours are every other line. So between 20 and 40, there is 1 interval (30), and between 40 and 60, 1 interval (50). So the contour interval is 10? Wait, that makes more sense. Wait, 20 to 30 is 10, 30 to 40 is 10, 40 to 50 is 10, 50 to 60 is 10. So the contour interval is 10. But the labels are 20, 40, 60, which are every 2 contour lines (since 20 + 2*10 = 40, 40 + 2*10 = 60). Ah, that's it! So the labeled contours are index contours (every 5th or every 2nd? Here, every 2nd, since 20, 40, 60: difference of 20, with 10 between each. Wait, no, 20 to 40 is 20, with one contour line in between (30), so the interval between 20 and 30 is 10, 30 and 40 is 10. So the contour interval is 10. Wait, I think I made a mistake earlier. Let's re-express:

Index contours (labeled) are every nth contour line, where n is the number of contour lines between index contours. So if index contours are 20, 40, 60, then the difference between index contours is 20, and the number of contour lines between them is 1 (since 20, [30], 40, [50], 60). So the contour interval (CI) is \( \frac{40 - 20}{1 + 1} \)? No, wait, the number of intervals between index contours is equal to the number of contour lines between them. So between 20 and 40, there is 1 contour line (30), so 1 interval. Wait, no, the number of intervals between 20 and 40 is 1 (since 20 to 30 is 1 interval, 30 to 40 is another? No, no: the contour interval is the difference between adjacent contour lines. So adjacent means next to each other. So if 20 and 30 are adjacent, CI is 10; 30 and 40 are adjacent, CI is 10. Then the index contours (labeled) are 20, 40, 60, which are every 2nd contour line (since 20 + 2*10 = 40, 40 + 2*10 = 60). So the contour interval is 10. But how to calculate it from the labeled contours?

Formula: CI = (Difference between two index contours) / (Number of contour lines between them + 1). Wait, no, the number of intervals between index contours is equal to the number of contour lines between them. So between 20 and 40, there is 1 contour line (30), so 1 interval. Wait, no, the number of intervals between 20 and 40 is 2? No, 20 to 30 is interval 1, 30 to 40 is interval 2? No, that's not right. The contour interval is the difference between adjacent (next to each other) contour lines. So if you have contour lines at elevations 20, 30, 40, 50, 60, then adjacent contours have a difference of 10 (30-20=10, 40-30=10, etc.). The index contours (labeled) are 20, 40, 60, which are every 2nd contour line (since 20, skip 30, label 40, skip 50, label 60). So the difference between index contours is 20, and the number of contour lines between them is 1 (30 between 20 and 40, 50 between 40 and 60). So the contour interval is \( \frac{40 - 20}{1 + 1} \)? No, that's not. Wait, the correct formula is: CI = (Elevation of higher index contour - Elevation of lower index contour) / (Number of contour intervals between them). The number of contour intervals between two index contours is equal to the number of contour lines between them. So between 20 and 40, there is 1 contour line (30), so 1 interval? No, 20 to 30 is 1 interval, 30 to 40 is another? No, I'm confused. Let's take a simple example: if index contours are at 100 and 200, with one contour line between them (150), then the contour interval is 50 (150-100=50, 200-150=50), and the difference between index contours is 100, with 1 contour line between, so number of intervals between index contours is 2 (100 to 150, 150 to 200). Wait, yes! So the number of intervals between index contours is equal to the number of contour lines between them plus 1? No, no: between 100 and 200, with 150 in between, there are two intervals: 100-150 and 150-200. So the number of intervals between index contours is (number of contour lines between them) + 1? No, the number of contour lines between 100 and 200 is 1 (150), so the number of intervals is 2 (100-150, 150-200). So the formula is: CI = (Higher index - Lower index) / (Number of intervals between them). The number of intervals between index contours is equal to the number of contour lines between them + 1? No, the number of intervals between two index contours is equal to the number of contour lines between them plus 1? Wait, no, if you have three contour lines: 100, 150, 200, then between 100 and 200, there are two intervals (100-150, 150-200), and one contour line between them (150 is between 100 and 200? No, 150 is between 100 and 200, so the number of contour lines between 100 and 200 is 1 (150), and the number of intervals is 2. So the formula is: CI = (200 - 100) / 2 = 50. Which matches. So in our problem, first map: index contours are 20, 40, 60. Let's take 20 and 40. The number of contour lines between them: looking at the map, between 20 and 40, how many contour lines? Let's see the first map: the outermost is 60, then inside is 40, then 20. Wait, maybe the labels are 20, 40, 60, with no contour lines between them? No, that can't be. Wait, maybe the first map has contour lines at 20, 40, 60, with no lines in between, meaning the contour interval is 20. But that seems too big. Wait, maybe the question is simpler: the difference between 60 and 40 is 20, 40 and 20 is 20, so the contour interval is 20. But I think I was overcomplicating with index contours. Maybe the map has contour lines labeled 20, 40, 60, with each adjacent pair having a difference of 20, so the contour interval is 20.

Wait, let's check the second map: the outermost is 140, and the innermost is, say, 200? No, the label is 140. Maybe the second map's contour interval is also 20? But maybe the first map: let's do the calculation again.

Contour interval (CI) = (Elevation of contour 2 - Elevation of contour 1) / (Number of contour lines between them + 1). Wait, no, the correct formula is that the contour interval is the vertical distance between adjacent contour lines. So if two adjacent contour lines have elevations h1 and h2, then CI = |h2 - h1|.

In the first map, we have contour lines labeled 20, 40, 60. Let's assume that the contour line labeled 40 is adjacent to the one labeled 20, so the difference is 40 - 20 = 20. Similarly, 60 - 40 = 20. So the contour interval is 20.

Yes, that makes sense. So the contour interval is 20.

Answer:

20