SOLUTION: At trench is 180 ft and 12 ft deep , 7 ft wide at the top, and 4 ft at the botton. How many cubic yard of earth been removed ?

Algebra ->  Surface-area -> SOLUTION: At trench is 180 ft and 12 ft deep , 7 ft wide at the top, and 4 ft at the botton. How many cubic yard of earth been removed ?      Log On


   

Question 947498: At trench is 180 ft and 12 ft deep , 7 ft wide at the top, and 4 ft at the botton. How many cubic yard of earth been removed ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
base 1=b1=7 ft, base 2=b2=4 ft, height=h=12 ft, Length=L
The cross section of the trench is a trapezoid
Area of a trapezoid=+A=%28%28b1%2Bb2%29%2F2%29%2Ah
The Volume (V)will equal cross sectional area times the length, so
Volume=%28%28b1%2Bb2%29%2F2%29%2Ah%2AL
V=%28%287ft%2B4ft%29%2F2%29%2A12ft%2A180ft
V=5.5ft%2A12ft%2A180ft
V=11880 cu ft
Convert the answer to cubic yards (27 cu ft=1 cu yd)
V=(11880 cu ft)(1 cu yd/27 cu ft)=440 cu yd
ANSWER: 440 cubic yards of dirt were moved to dig the trench.