A 120 ft long Type C trench is cut with a 4 ft bottom width and a 6 ft depth. If side slopes are 1-1/2 horizontal to 1 vertical, what excavation volume is closest?
Correct Answer
A) 347 cy
Each side widens 1.5 x 6 = 9 ft, so top width is 4 + 18 = 22 ft. Average width is (4 + 22)/2 = 13 ft. Volume is 120 x 13 x 6 = 9,360 cf, and 9,360/27 = 346.7 cy, or about 347 cy. Other choices use the bottom width only, one side slope only, or a 1H:1V slope.
Why This Is the Correct Answer
Each side widens 1.5 x 6 = 9 ft, so top width is 4 + 18 = 22 ft. Average width is (4 + 22)/2 = 13 ft. Volume is 120 x 13 x 6 = 9,360 cf, and 9,360/27 = 346.7 cy, or about 347 cy. Other choices use the bottom width only, one side slope only, or a 1H:1V slope.
Why the Other Options Are Wrong
Option B: 267 cy
sloped excavation volume, choice a: 267 cy implies about 222.5 percent fall over 120 ft; the stated slope is the one used in.
Option C: 293 cy
sloped excavation volume, choice b: 293 cy is wrong because 293 cy implies about 244.17 percent fall over 120 ft; the stated slope is the one used in.
Option D: 320 cy
sloped excavation volume, choice c: 320 cy implies about 266.67 percent fall over 120 ft; the stated slope is the one used in.
Memory Technique
Remember sloped excavation volume as "base, adjustment, final unit"; the last unit should read 347 cy.
Reference Hint
Open 29 CFR Part 1926, Subpart P - Excavations; use 29 CFR 1926 Subpart P Appendix B, Table B-1; excavation volume calculation to confirm that Each side widens 1.5 x 6 = 9 ft, so top width is 4 + 18 = 22 ft.
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