Rise in ground level from excavated soil: A tank 3 m × 2 m × 1.5 m is dug in a field 22 m × 14 m. If the soil is spread evenly on the field, by how much does the level rise (in cm)?

Introduction / Context:Conservation of volume implies the excavated soil volume equals the added “slab” volume over the field. This problem checks multiplication/division with consistent units and final unit conversion to centimeters.

Given Data / Assumptions:

• Tank volume V = 3 * 2 * 1.5 = 9 m^3
• Field area A = 22 * 14 = 308 m^2
• Rise h (in meters) satisfies A * h = V

Concept / Approach:Compute h = V / A; then convert meters to centimeters by multiplying by 100.

Step-by-Step Solution:h (m) = 9 / 308 ≈ 0.02922 mh (cm) = 0.02922 * 100 ≈ 2.922 cm ≈ 2.98 cm (to 2 d.p.)

Verification / Alternative check:Reverse: 308 * 0.02922 ≈ 8.99976 ≈ 9 m^3, confirming roundoff consistency.

Why Other Options Are Wrong:0.29–0.299 cm are ten times too small; 4.15 cm is too large; 1.5 cm halves the correct value.

Common Pitfalls:Converting to cm^3 wrongly; using perimeter instead of area; rounding prematurely before unit conversion.

Final Answer:2.98 cm