Earthwork spread — rise of ground level: A rectangular tank 30 m long, 20 m wide, and 12 m deep is excavated in a field 500 m long and 30 m wide. If the excavated earth is spread evenly over the entire field, by how much (in meters) will the field level rise?

Introduction / Context:
When excavated soil is uniformly spread over a larger area, the rise in ground level equals volume of excavation divided by the spread area. This is a direct volume-conservation application.

Given Data / Assumptions:

• Tank: 30 m × 20 m × 12 m.
• Field: 500 m × 30 m.
• All excavated earth is spread across the whole field without loss.

Concept / Approach:
Let V be the excavated volume and A be the field area. Then rise h = V / A.

Step-by-Step Solution:
Excavation volume V = 30 * 20 * 12 = 7200 m3Field area A = 500 * 30 = 15000 m2Rise h = V / A = 7200 / 15000 = 0.48 m

Verification / Alternative check:
Unit analysis: m3 / m2 = m, consistent for a height rise.

Why Other Options Are Wrong:
0.5 m and 0.4 m are rounded or underestimated; 0.33 m assumes a different area or volume.

Common Pitfalls:
Mixing up field dimensions, omitting unit conversion, or restricting spreading only to some part of the field.

Final Answer:
0.48 m