# Volume of Holes Left by a Tree Spade

From my e-mail:

Greetings Sir,

My name is Michael ______ and I am a resident in _______, Florida.

I have a question in which you may be able to help.

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.

How would you respond? Recognize that he wants to know "How much?" but he also needs to understand how you arrived at your answer.

A. Would you calculate the volume first in Cubic Inches? Cubic Feet? Cubic yards?   WHY?

B. How many cubic inches in a cubic foot? (1296)
How many cubic inches in a cubic yard?  (46656)
How can you avoid needing to use either of these bits of information?  (other than 'avoiding' by choosing not to work on the problem)

Do not multiply.  Leave in factored form and reduce the fraction.

C. Fill dirt is purchased by the truck load. There are 6 cubic yards in a truck load (for the available trucks at the company providing the fill dirt). How many truck loads would you order? (Note: The answer must be an integer value. The company will not supply a fraction of a truck load.)

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