A near 1000 ft long ___ inch diameter PVC pipeline is to be installed in a rocky area. A 24 inch wide trench was excavated to a depth of 4 ft. How many cubic yards of bedding sand will be required to provide sand encasement around the pipe for a total depth of 24 inches, assuming 12 inches of bedding is to be replaced below the pipe?

• A. 120 cubic yards
• B. 150 cubic yards
• C. 135 cubic yards
• D. 160 cubic yards

Answer: (C)

Calculating bedding sand volume uses the idea that the sand around the pipe fills a rectangular prism along the length of the pipe, minus the space occupied by the pipe itself.

Convert dimensions to feet: trench width = 24 inches = 2 ft, sand depth (bedding) = 24 inches = 2 ft, and pipe diameter is 8 inches = 0.6667 ft, so the pipe’s cross-sectional area is π(0.3333 ft)^2 ≈ 0.349 ft^2.

Cross-sectional area of sand per unit length = trench width × sand depth − pipe area = 2 ft × 2 ft − 0.349 ft^2 = 4 − 0.349 ≈ 3.651 ft^2.

Volume along the full length (1000 ft) = 3.651 ft^2 × 1000 ft ≈ 3651 ft^3.

Convert to cubic yards: 3651 ft^3 ÷ 27 ≈ 135 yd^3.

So about 135 cubic yards of bedding sand are needed.