Creating a berm with a 1:1 slope

[thatboygood]

Homework Statement

324,000 cubic feet of soil is to be placed in a rectangular area (constructed from hay bales) of 80 feet x 100 feet. Using a slope of 1:1 for the fill soil, how many bales high must the walls be stacked to accommodate the soil?
Assume the hay bales have a height of 18"

Homework Equations

A = L x W
V = A x h

Volume of a pyramid...? 1/3(L x W x h) = V

The Attempt at a Solution

I started by calculating the required height (assuming the soil was filled without a slope):

324,000 cu ft = 8000ft x h
h = 40.5 ft

I know from here I would simply divide the total height (h) by the height of a hay bale (18"), to get the number of bails. However, I am thinking that my calculated height is too much, since the soil will be slopped (1:1 slop) and extend above the walls. My question is, how do I figure out how high the soil can be slopped above the walls? and what the volume of soil extending above the walls would be. I was thinking this may have something to do with calculating the volume of a pyramid... but I'm a bit confused as to how to proceed. Any help or suggestions would be greatly appreciated.

 

[Mark44]

Homework Statement

32,400 cubic feet of soil is to be placed in a rectangular area (constructed from hay bales) of 80 feet x 100 feet. Using a slope of 1:1 for the fill soil, how many bales high must the walls be stacked to accommodate the soil?
Assume the hay bales have a height of 18"

Homework Equations

A = L x W
V = A x h

Volume of a pyramid...? 1/3(L x W x h) = V

The Attempt at a Solution

I started by calculating the required height (assuming the soil was filled without a slope):

324,000 cu ft = 8000ft x h
h = 40.5 ft

The problem says 32,400 cu ft.

I know from here I would simply divide the total height (h) by the height of a hay bale (18"), to get the number of bails. However, I am thinking that my calculated height is too much, since the soil will be slopped (1:1 slop) and extend above the walls. My question is, how do I figure out how high the soil can be slopped above the walls? and what the volume of soil extending above the walls would be. I was thinking this may have something to do with calculating the volume of a pyramid... but I'm a bit confused as to how to proceed. Any help or suggestions would be greatly appreciated.

 

[thatboygood]

The problem says 32,400 cu ft.

That was a typo. Thanks for pointing it out. I have corrected it in my original post.

 

[Mark44]

Do you have an idea of how the berm will look, with its sloped (not slopped) sides?

 

[thatboygood]

Do you have an idea of how the berm will look, with its sloped (not slopped) sides?

When sloped, it should resemble a pyramid.

 

[Mark44]

OK.
The problem would be a bit easier if the base happened to be square, rather than rectangular.