EMAT 6600

Problem Solving

Solution: Since we
going to need the result of all this in cubic feet, let us convert the inches
into yards. 90 inches = 7.5 feet and 60 inches = 5 feet. To find how much
back-fill it will require for each hole, we calculate the volume of the
hole. Since the hole is canonical, the
volume is 1/3 pr^{2}h.
The volume of the hole is 1/3p(3.75)^{2}*5 = 73.63 cubic feet. Since there are 27 cubic feet/cubic yard, we
can now convert the volume of one cone to cubic yard. So, the volume of one cone is approximately 2.73 cubic yard. Multiply that by 150 and we obtain
approximately 409 cubic yard to do the entire job.

To find the cubic inches in a cubic foot, consider the scale that 1 cubic inch = 0.000578703704. So, in a cubic foot there are 1727.9999991152640004529848317681 which is approximately 1728 cubic inches.

There 6 cubic yards a truck, and we need approximately 409 cubic yards. Then, we would have to order 69 trucks of fill.