Earthwork spread from a cylindrical ditch\nA square field has area X m². A cylindrical ditch of radius 7 m and depth 2 m is dug; the removed earth is spread uniformly over the remaining part of the field (excluding the circular ditch), raising its level by 0.77 m. Find X.

Introduction / Context:
Conservation of volume applies: soil removed from the cylindrical ditch equals the volume added to the remaining area as a uniform layer. Care is needed to subtract the hole’s plan area when determining where the soil is spread.

Given Data / Assumptions:

• Radius r = 7 m, depth h = 2 m
• Rise over remaining area = 0.77 m
• Use π = 22/7 for neat integers.

Concept / Approach:
Volume removed V = π r^2 h. Remaining area = X − π r^2. By conservation: V = (X − π r^2) * 0.77. Solve for X in m².

Step-by-Step Solution:

Verification / Alternative check:
Plug back: remaining area = 554 − 154 = 400; 400 * 0.77 = 308, which matches removed volume exactly.

Why Other Options Are Wrong:
Values other than 554 fail the exact conservation equation with π = 22/7. 554 is the unique match.

Common Pitfalls:
Spreading soil over the whole square (including the ditch) or using the wrong π approximation can skew the result.

Final Answer:
554 sq. m