Question #206195

*The railroad cut shown in the figure has sides inclined at 45 degrees to the horizontal. the base of the cuts is a horizontal rectangle and the ends are vertical. the depth of the cut at each of the points A, B, C, D is indicated in the figure. Find the cost of the making the cut at 1 dollars per cube yard*

Expert's answer

If we can assume the diagram given to be a triangular prism

Surface area "=bh \\times 2ls \\times lb"

Where l=10ft; s=5 ft

Then "sin \\theta =\\frac{h}{H} \\implies sin 45^0 = \\frac{h}{5} \\implies h=5 sin 45 = 3.5 ft"

Similarly we can find the base, "b^2+h^2=H^2 \\implies b= \\sqrt{5^2-3.5^2}=3.6 ft"

Therefore, the full length of the base is "3.6 \\times 2 =7.2 ft"

"SA=bh \\times 2ls \\times lb =7.2 \\times 3.5+2\\times10\\times5+10\\times3.6 = 161.2 ft sq"

Also we can find the volume of the figure above

"V= A\\times h = 161.2 \\times 3.5 = 564.2 ft^3"

Cube foot to cube yards

1 Cube foot 0.037037 cube yards

564.2 Cube foot = 20.896296 cube yards

The cost will be

1 cube yards = $ 1

20.896296 cube yards = $ 20.896296

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