← BACK PRINT + TEXT SIZE SEARCH HOME
Math CentralQuandaries & Queries

search

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!
RD

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS