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 Question from Donnie: I need to know the formula to figure cubic yds of fill dirt to fill an area from 4ft. deep to 18 inches deep this lot is on a slope and I am wanting to level 176 ft long by 4ft. deep the sides is 115 ft. wide the upper side is 18 inches deep.

Donnie,

The volume is the area of the cross-section times te width of 115 feet. The shape of the cross-section is a trapezoid, a figure bounded by 4 lines, two of which are parallel. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. You have parallel sides of length 4 and 18 inches but you don't know the distance between them. It should be close to 176' but lets find it more exactly.

Before I begin I am going to change all the dimensions to yards since you asked for the volume in cubic yards. In yards the dimensions arre 176/3 = 58.67, 115/3 = 38.33, 18/36 = 0.50 and 4/36 = 0.11.

To find the distance between the parallel sides d I am going to use Pythagoras theorem.

Triangle ABC is a right triangle |BC| = 58.67 yards, |CA| = 0.5 - 0.11 = 0.39 yards and |AB| = d yards. Thus

0.392 + d2 = 58.672

and hence

d = √(58.672 - 0.392) = 58.67 yards.

Thus two 2 decimal places d and |BC| are the same length.

The area of the trapezoidal cross-section is thus

[(0.50 + 0.11)/2] × 58.67 = 17.89 square yards.

Finally the volume of fill you need is 17.89 × 38.33 = 686 cubic yards.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.