Math CentralQuandaries & Queries


Question from Dean:
The only place I have to deliver gravel is in my driveway.
The driveway is 16 ft wide by 18 ft long.
How much gravel can I order as to not exceed the boundaries of my driveway
when the truck dumps the gravel onto my driveway?
I am assuming the angle of repose comes into play
when calculating this elliptical pile?
The maximum amount of gravel I need is 12 cubic yards.

Firstly, I would drop the assumption that the pile must be elliptical; a truck should be able to dump gravel fairly uniformly over a rectangle.

Now, the angle of repose will depend on many things, but I think 30 degrees or better is a safe assumption. That means the height of the pile will be at least 1/4 its minimum width.

A pyramid 16' x 16' x 4' contains about 12.5 yards of gravel,

16 x 16 x 4 x (1/3) x (1/27)

so you should be OK, if the driver starts dumping in the middle of the drive and comes forward just a little as it's tipping. With damp crusher-run gravel I'm guessing you might get close to 45 degrees and it might actually need spreading to the side if the truck bed is low.

Good luck!

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