EMAT 6600

Problem Solving




Volume of Holes Left by a Tree Spade

I have sold some large cedar trees to be used for landscaping. The contractor promised to fill in the holes he's dug after he's taken the trees out. He used a 90-inch hydraulic tree-digging spade, so the base of the cone is 90-inches across at its widest, and approximately 60-inches deep. How much back-fill will be required to fill each individual hole, or how much fill would be required to do the entire job, assuming he removes 150 trees. Fill is supplied in cubic yards, that I'm sure you know is 27-cubic feet/cubic yard.

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 pr2h. 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.