A grading plan shows contour lines spaced 2 feet apart vertically. If the horizontal distance between two adjacent contour lines is 40 feet, what is the slope percentage?
Correct Answer
A) 5%
Slope percentage = (vertical rise ÷ horizontal run) × 100. Slope = (2 feet ÷ 40 feet) × 100 = 5%. This represents a relatively gentle slope suitable for most construction activities.
Why This Is the Correct Answer
Option B is correct because slope percentage is calculated using the formula (vertical rise ÷ horizontal run) × 100. With a vertical rise of 2 feet between contour lines and a horizontal distance of 40 feet, the calculation is (2 ÷ 40) × 100 = 5%. This represents the grade or steepness of the terrain between the two contour lines.
Why the Other Options Are Wrong
Option B: 40%
Option A (2%) incorrectly uses only the vertical rise without dividing by the horizontal run, or represents a calculation error in the slope formula.
Option D: 20%
Option C (20%) incorrectly reverses the calculation by dividing horizontal run by vertical rise (40 ÷ 2 = 20), which is the inverse of the correct slope formula.
Memory Technique
Remember 'RRH' - Rise over Run times Hundred. Also think 'small rise, big run = gentle slope' to check if your answer makes sense (5% is indeed a gentle slope).
Reference Hint
Look up 'Site Work and Grading' or 'Topographic Maps and Contour Lines' in your construction reference manual, typically found in the site preparation or surveying sections.
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