How much aggregate backfill would be used for a 3' x 5' x 4,000' trench with a 1 inch diameter pipe?

How much aggregate backfill would be used for a 3' x 5' x 4,000' trench with a 1 inch diameter pipe?

• A. 56,860 cu ft
• B. 60,000 cu ft
• C. 59,978 cu ft
• D. 56,000 cu ft

Answer: (A)

Backfill volume comes from the trench volume minus the volume occupied by the pipe along the length. For a rectangular trench, volume = width × depth × length. So 3 ft × 5 ft × 4,000 ft = 60,000 cubic feet. The pipe is a cylinder with a 1 inch diameter. Radius is 0.5 inch = 0.5/12 = 0.0416667 ft. Cross-sectional area = πr^2 ≈ π × (0.0416667)^2 ≈ 0.005450 ft^2. Over 4,000 ft, pipe volume ≈ 0.005450 × 4,000 ≈ 21.8 cubic feet. Subtracting: 60,000 − 21.8 ≈ 59,978 cubic feet of aggregate backfill.

Backfill volume comes from the trench volume minus the volume occupied by the pipe along the length.

For a rectangular trench, volume = width × depth × length. So 3 ft × 5 ft × 4,000 ft = 60,000 cubic feet.

The pipe is a cylinder with a 1 inch diameter. Radius is 0.5 inch = 0.5/12 = 0.0416667 ft. Cross-sectional area = πr^2 ≈ π × (0.0416667)^2 ≈ 0.005450 ft^2. Over 4,000 ft, pipe volume ≈ 0.005450 × 4,000 ≈ 21.8 cubic feet.

Subtracting: 60,000 − 21.8 ≈ 59,978 cubic feet of aggregate backfill.