A grading plan shows contour lines at 2-foot intervals. If you count 6 contour lines between two points that are 240 feet apart horizontally, what is the slope percentage between these points?
Correct Answer
C) 5%
The elevation change is 6 contour lines × 2 feet = 12 feet. Slope percentage = (rise/run) × 100 = (12/240) × 100 = 5%. This represents a relatively gentle slope.
Why This Is the Correct Answer
To calculate slope percentage, use the formula (rise/run) × 100. The rise is 6 contour lines × 2-foot intervals = 12 feet of elevation change. The run is the horizontal distance of 240 feet. Therefore: (12 ÷ 240) × 100 = 0.05 × 100 = 5%. This represents a gentle slope commonly found in residential grading projects.
Why the Other Options Are Wrong
Option A: 10%
This answer incorrectly calculates the slope as 10%. This error likely comes from miscalculating the elevation change or horizontal distance. The correct calculation is (12 ÷ 240) × 100 = 5%, not 10%.
Option B: 12%
This answer of 12% is incorrect and may result from confusing the total elevation change (12 feet) with the slope percentage. The slope percentage requires dividing rise by run, then multiplying by 100.
Option D: 15%
This answer of 15% is incorrect and significantly overestimates the slope. This error might occur from incorrectly calculating either the rise or run values, or from misunderstanding the slope percentage formula.
Memory Technique
Remember 'Rise over Run times 100' - like climbing stairs: count the vertical steps (rise), measure the horizontal distance (run), then convert to percentage.
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