How do you calculate the volume of backfill for a trench with length, width, and depth?

How do you calculate the volume of backfill for a trench with length, width, and depth?

• A. Volume = length × width ÷ depth.
• B. Volume = (length + width) × depth.
• C. Volume = length × width + depth.
• D. Volume = length × width × depth.

Answer: (D)

Volume for a trench is found by multiplying its base area by its depth. For a rectangular trench, the base area is length times width, so the volume is length × width × depth. This gives cubic units (e.g., cubic meters), which is what you need for backfill. Why the other forms don’t fit: length × width ÷ depth would give a linear dimension, not a volume. (length + width) × depth and length × width + depth mix dimensions in ways that don’t produce volume (units don’t come out in cubic meters). The product of all three dimensions correctly represents the space the backfill must fill. For example, a trench 10 m long, 2 m wide, and 1.5 m deep holds 10 × 2 × 1.5 = 30 m³ of backfill.

Volume for a trench is found by multiplying its base area by its depth. For a rectangular trench, the base area is length times width, so the volume is length × width × depth. This gives cubic units (e.g., cubic meters), which is what you need for backfill.

Why the other forms don’t fit: length × width ÷ depth would give a linear dimension, not a volume. (length + width) × depth and length × width + depth mix dimensions in ways that don’t produce volume (units don’t come out in cubic meters). The product of all three dimensions correctly represents the space the backfill must fill. For example, a trench 10 m long, 2 m wide, and 1.5 m deep holds 10 × 2 × 1.5 = 30 m³ of backfill.