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