For a trench measuring 5 feet wide by 60 feet long with a slope from 0 to 8 feet, the excavation volume is in which range?

For a trench measuring 5 feet wide by 60 feet long with a slope from 0 to 8 feet, the excavation volume is in which range?

• A. 43.1 to 46 cubic yards
• B. less than 40 cubic yards
• C. 40 to 43 cubic yards
• D. greater than 46 cubic yards

Answer: (A)

When depth changes linearly along the trench, you can use the average depth to find the volume. The depth goes from 0 to 8 feet, so the average depth is (0 + 8) / 2 = 4 feet. The trench footprint is 5 feet wide by 60 feet long, which is 300 square feet. Multiply by the average depth: 300 ft^2 × 4 ft = 1200 ft^3. Converting to cubic yards (1200 ÷ 27) gives about 44.4 cubic yards, which lies in the range 43.1 to 46 cubic yards.

When depth changes linearly along the trench, you can use the average depth to find the volume. The depth goes from 0 to 8 feet, so the average depth is (0 + 8) / 2 = 4 feet. The trench footprint is 5 feet wide by 60 feet long, which is 300 square feet. Multiply by the average depth: 300 ft^2 × 4 ft = 1200 ft^3. Converting to cubic yards (1200 ÷ 27) gives about 44.4 cubic yards, which lies in the range 43.1 to 46 cubic yards.