How many cubic yards of backfill are required for a 3' x 5' trench, 1500 ft long, with a 1-foot diameter pipe?

How many cubic yards of backfill are required for a 3' x 5' trench, 1500 ft long, with a 1-foot diameter pipe?

• A. 650.00 cubic yards
• B. 502.35 cubic yards
• C. 789.72 cubic yards
• D. 1200.00 cubic yards

Answer: (C)

Backfill volume is the trench space around the pipe, so you subtract the pipe’s volume from the trench’s volume and then convert to cubic yards. Trench cross-section area: 3 ft × 5 ft = 15 ft². Trench volume: 15 ft² × 1500 ft = 22,500 ft³. Pipe is a cylinder with diameter 1 ft, radius 0.5 ft, length 1500 ft. Pipe volume: π r² h = π × (0.5)² × 1500 = 375π ≈ 1,178.1 ft³. Backfill volume: 22,500 ft³ − 375π ft³ ≈ 21,321.9 ft³. Convert to cubic yards: 21,321.9 ÷ 27 ≈ 789.7 yd³. So the required backfill is about 789.7 cubic yards, which matches the option 789.72 cubic yards.

Backfill volume is the trench space around the pipe, so you subtract the pipe’s volume from the trench’s volume and then convert to cubic yards.

Trench cross-section area: 3 ft × 5 ft = 15 ft².

Trench volume: 15 ft² × 1500 ft = 22,500 ft³.

Pipe is a cylinder with diameter 1 ft, radius 0.5 ft, length 1500 ft.

Pipe volume: π r² h = π × (0.5)² × 1500 = 375π ≈ 1,178.1 ft³.

Backfill volume: 22,500 ft³ − 375π ft³ ≈ 21,321.9 ft³.

Convert to cubic yards: 21,321.9 ÷ 27 ≈ 789.7 yd³.

So the required backfill is about 789.7 cubic yards, which matches the option 789.72 cubic yards.