A cartographer creates a topographic map using contour lines every 10 meters. A hill rises from 120 meters to 680 meters above sea level. How many contour lines (including both elevations) appear on the map?

Creating Accurate Topographic Maps: Understanding Contour Lines

A topographic map is an essential tool for cartographers, hikers, geologists, and urban planners. It visually represents elevation changes across a landscape using contour lines—imaginary lines connecting points of equal elevation above sea level. One common practice is defining contour intervals that simplify terrain interpretation while maintaining precision.

The hill in focus rises from 120 meters to 680 meters above sea level. With a standard contour interval of 10 meters, cartographers carefully determine how many contour lines appear on the map. But how is this calculated?

Understanding the Context

Understanding Contour Lines and Intervals

Contour lines mark specific elevation levels. For example, every 10 meters—120 m, 130 m, 140 m—up to 680 m—each represents a distinct elevation. Since the base elevation is 120 m and the peak reaches 680 m, the total vertical rise is:

680 m – 120 m = 560 meters

With a 10-meter contour interval, the number of elevation steps is:

A cartographer creates a topographic map using contour lines every 10 meters. A hill rises from 120 meters to 680 meters above sea level. How many contour lines (including both elevations) appear on the map?

Key Insights

560 ÷ 10 = 56 intervals

However, contour lines are drawn at each elevation point, including both the starting and ending points. This means the first contour line appears at 120 m, and the last at 680 m, spanning exactly 56 intervals.

Total Number of Contour Lines

Because each elevation increment corresponds to a single contour line, and both endpoints are included, there are 57 contour lines on the map.

Visual and Practical Implications

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Final Thoughts

This structured elevation representation helps hikers gauge steepness, engineers plan construction, and scientists model watersheds or land degradation. Precision in selecting interval size—like 10 meters—ensures clarity without cluttering the map.

In summary:

Start: 120 m
End: 680 m
Elevation range: 560 m
Contour interval: 10 m
Contour lines drawn at: 120, 130, ..., 680 (inclusive)
Total contours: 120 → 130 → ... → 680 = (680 – 120)/10 + 1 = 57 lines

This methodical approach underscores the cartographer’s role in transforming raw terrain into actionable geographic knowledge.

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Use this detailed breakdown to enhance understanding of how contour lines symbolize elevation—and how cartographers determine how many to include on a topographic map.