Question

In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill? 

 

• A. P
• B. Q
• C. R
• D. S

Hint:

Remember the fundamental rule of contour maps: {Closely spaced lines = Steep slope}, and {Widely spaced lines = Gentle slope}. Always analyze the symmetry and steepness of the given profile first.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires interpreting a 2D side-profile graph of a hill and translating it into a 2D top-view contour map. A contour map represents a 3D shape on a 2D surface using contour lines, where each line connects points of equal elevation. The spacing between contour lines indicates the steepness of the slope.
Step 2: Detailed Explanation:
1.Analyze the Side-Profile Graph: The graph shows the height (\(h\)) of the hill versus the horizontal distance. The hill is not symmetric.
The left side of the hill (from distance 0 to the peak at approx. 0.3 km) is very steep. The height changes rapidly over a short horizontal distance. The right side of the hill (from the peak at approx. 0.3 km to 1.0 km) has a much gentler slope. The height changes slowly over a long horizontal distance.
2.Relate Slope to Contour Lines:
Steep Slope: On a contour map, a steep slope is represented by contour lines that are very close together.
Gentle Slope: A gentle slope is represented by contour lines that are far apart.
3.Evaluate the Options (Top Views):
P: The contour lines are spaced symmetrically, implying the hill has slopes of equal steepness on both sides. This contradicts the graph.
Q: The contour lines on the left side (corresponding to the start at 0 km) are close together, indicating a steep slope. The lines on the right side are spread far apart, indicating a gentle slope. This perfectly matches the profile shown in the graph.
R: The contour lines on the left are far apart (gentle slope) and the lines on the right are close together (steep slope). This is the opposite of the hill shown in the graph.
S: The contour lines are spaced symmetrically, similar to P, but elongated differently. This contradicts the asymmetric nature of the hill.
Step 4: Final Answer:
Option Q correctly depicts the top view of the hill.
Step 5: Why This is Correct:
The side profile clearly shows a steep ascent on the left and a gentle descent on the right. In a contour map, this translates to closely packed contour lines for the steep part and widely spaced lines for the gentle part. Only option Q displays this characteristic.