Answer to Question #206195 in Civil and Environmental Engineering for John

Question

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

Answer 1

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