Mathematical task: the amount of concrete for a pyramid

[HarveyH43]

Mathmatic nightmare...

Well, I'll admit this is a little weird and out of place, but figured I'd give it shot.

I'm trying to buid a small pyramid with concrete, as a headstone. Inbeded in one side will be a small LCD screen displaying a slideshow of some photographs.

The concrete form is way out of my league, but managed to learn what I need to calculate the volume of the pyramid and how much concrete I'll need. But, I have no idea how to go about figuring the the angles I'll need for the edge cuts on the plywood form. When I first got this idea, I figured a 45 degree angle, like a picture frame (four sides, half the 90 degree corners). But, as I get closer to actually start construction, the feel that it's not quite right gets stronger.

I'm thinking that the base angle of the pyramid will need to be considerd in the angle cuts on the plywood....

Anyway, the base is 36 inches square, each side is an equalateral triangle. The form will be built lay on one side (front suface). The backside facing up an parallel to the ground I'll need 36 inch square for the base, and 3 triangles. The edges most meet cleanly. The base square is simple, half the base angle, but the triangles....

Yeah, it will weigh a lot, but I'm guessing that it will be sitting near equalibrium, and I should be able support or anchor as needed. After concrete cures, just remove the base square, and let gravity do the rest, with minimal help

Oh, guess I should mention, it's a marker for my dog... But still an interesting challenge if you good with math. Any help would be appreciated. As you can imagine, not something with many resources on the web...

 

[lladnar23]

Re: Mathmatic nightmare...

HarveyH43,

You were correct the first time about the 45 degree angles -- You should cut each equilateral triangle to have a 45 degree edge on all three sides. This solution can be pictured mentally by viewing the pyramid from the square base. Just like the picture-frame, the square base requires 45 degree cuts, and this does not change for a bigger or smaller pyramid. So by thinking of the pyramid as a stack of 1-dimentional square "picture-frames", each one slightly smaller than the previous one, it is easy to see that the edges of the triangle sides need to also be 45 degrees.

Best of luck!

 

[HarveyH43]

Re: Mathmatic nightmare...

Thanks. I'll buy the plywood and 2X4s this week, and work on it over the weekend. Very relieved, 45 degree cuts are rough enough without a table saw. Wonder if Home Depot would do it cheap...

Anyway, weather permitting, shouldn't take half a day.

Thanks again.

 

[HarveyH43]

Re: Mathmatic nightmare...

Well, I know it's been a while, but it's finished and set into place. Turned better than expected.

I really blew it on calculating how much concrete I would need to fill the form. I mixed 11 X 80 lbs bags of concrete, and still needed more. It was obvious at bag number 10, so I grabbed everything concrete (fortunately I saved a lot of pewter molds) and stuffed them in. Even the last bag came up a little short, about a half inch. Figured close enough, that would be the backside face.

Setting it into place was so simple, it turned out to be very well balanced. So close to equalibrium. Used a 2 X 4 as a lever to rock it forward enough to remove the for from the base. Just out of curiosity, I tried to just lift the point, which came up easy. So just lifted it over into place.

The recess for the pewter plaque was a problem, the plywood was stuck in pretty good, had to use a hammer and screwdriver. The plaque fit tight, but didn't need to beat on it.

Anyway, thanks for the help.