Hydrology – Basin shape metric:\r If the axial length (basin length) of a drainage basin is 35 km and its form factor is 0.2, compute the total catchment area in square kilometres. Use the standard definition: form factor F = A / L^2.

Introduction / Context:
Form factor is a widely used hydrologic shape index that relates a basin’s planform geometry to its hydrologic response. It helps infer flood peaks and runoff concentration time from simple geometric inputs (area and length). This question tests the ability to apply the basic relationship between form factor, basin length, and area.

Given Data / Assumptions:

• Basin length L = 35 km (axial length along the principal flow path).
• Form factor F = 0.2 (dimensionless).
• Definition: F = A / L^2, where A is basin area (sq. km) and L is basin length (km).

Concept / Approach:
Form factor compresses shape information into a single number. For two basins of the same area, a larger F indicates a more circular shape and typically a flashier hydrograph. The computation is a direct substitution into the formula F = A / L^2, rearranged to A = F * L^2.

Step-by-Step Solution:
Write formula: F = A / L^2.Rearrange: A = F * L^2.Substitute values: A = 0.2 * (35)^2.Compute (35)^2 = 1225.So, A = 0.2 * 1225 = 245 sq. km.

Verification / Alternative check:
If F were 1.0 (a perfectly compact shape, hypothetical), A would equal L^2 = 1225 sq. km, which is much larger. Since the given F is 0.2, area must be a smaller fraction of 1225, namely 245 sq. km, confirming the calculation is consistent.

Why Other Options Are Wrong:

• 205, 215, 225, 235 sq. km: Each results from using an incorrect factor or arithmetic error; only 245 sq. km satisfies A = 0.2 * 1225.

Common Pitfalls:

• Confusing form factor with elongation ratio or circularity ratio.
• Using diameter instead of basin length, or mixing units.
• Forgetting the square on length in A = F * L^2, leading to large errors.

Final Answer:
245 sq. km