An engineer designed a 620 ft long water canal to drain a rainwater detention pond. It is to have a trapezoid cross-section that is 8 ft deep, 15 ft across the bottom, with walls sloping outward at an angle of 40.
(a)Calculate the volume of earth that needs to be excavated for this canal in m3.
(b)If a contractor places a bid to excavate this canal for $200/cubic yard plus 12% tax, how much will it cost?
Draw a figure.
At each end of the trapezoid there is a triangle of height 8, width x, where x/8 = tan 40 deg.
x = 6.7ft
So, the top of the trapezoid is 15 + 2x = 28.2 ft
The area of the trapezoid is thus 8*(15+28.2)/2 = 172.8 ft^2
The volume of the ditch is thus 620*172.8 = 10713.6 ft^3
The cost is thus 10713.6/27 * 200 * 1.12 = $88,883.20