Question

If a road elevation changes 10 m over a horizontal distance of 100 m, the slope will be: [Question ID = 1488][Question Description = 148_6_PHSC_AUG22_Q48]

• A. 0.01%
• B. 0.1%
• C. 1%
• D. 10%

Hint:

Be careful with units. Both rise and run must be in the same units. Also, don't confuse percentage slope with slope angle in degrees (\( \tan \theta = \text{rise/run} \)).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Slope is a measure of the steepness of a surface. It is defined as the ratio of the vertical change (rise) to the horizontal change (run).
Key Formula or Approach:
The percentage slope is calculated using the following formula:
\[ \text{Slope (\%)} = \left( \frac{\text{Vertical Rise}}{\text{Horizontal Run}} \right) \times 100 \]

Step 2: Detailed Explanation:
In the given problem, the values are:
- Vertical Rise = 10 m
- Horizontal Run = 100 m
Plugging these values into the formula:
\[ \text{Slope (\%)} = \left( \frac{10\ m}{100\ m} \right) \times 100 \]
\[ \text{Slope (\%)} = 0.1 \times 100 \]
\[ \text{Slope (\%)} = 10\% \]
This means for every 100 meters of horizontal travel, the ground rises by 10 meters. This is a common method of expressing gradients in soil surveys and engineering.

Step 3: Final Answer:
The calculated slope percentage is 10%.