trying to figure volume of a hopper (a truncated pyramid?)
Top to be 3ft square, bottom 2ft square, height 3ft.
Thanks.
trying to figure volume of a hopper (a truncated pyramid?)
Top to be 3ft square, bottom 2ft square, height 3ft.
Thanks.
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Replies
I don't know how a mathematician would do it but;
The area of a triangle is 1/2 the area of the rectangle it fits in. A pyramid is 1/2 the volume of the cubical block it fits in.
So:
Remove the 2'x2'x3' section in the middle. 2'x2'x3' = 12 cuft
slide the 2' wide center section of two opposite side in to meet. This gives a tringular section 1'x3'x 2' thick. 1/2 of 1x3x2 = 3 cuft.
Repeat for the other two sides = another 3 cuft.
This leaves the corners at 6"x6"x3' each or one pyramid 1'x1'x3' tall. 1/2 of 1x1x3 is 1.5 cuft.
12+3+3+1.5 = 19.5cuft.
I think. Maybe?
SamT
>> A pyramid is 1/2 the volume of the cubical block it fits in.All my references say 1/3.Volume of pyramid = ((area of base) * height) / 3The way I would do it is calculate the volume of the whole pyramid, then calculate the volume of the part you cut off.whole pyramid is ((3 * 3) * 9) / 3 = 27 cu ft
cut off part is ((2 * 2) * 6) / 3 = 8 cu ft
hopper is 27 - 8 = 19 cu ft
Thanks, guys I just could not remember the formula for volume of a pyramid.
My Bad....
...
...This leaves the corners at 6"x6"x3' each or one pyramid 1'x1'x3' tall. 1/3 of 1x1x3 is 1 cuft.12+3+3+1 = 19 cuft.SamT
18 cf but I did it in my head, so don't count on it
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I concur with those who say 19 cf in accordance with the following formula:
Where a and b are the lengths of the sides of the top and bottom squares (3 and 2) and h is the height (3). This assumes that your 3' height is the plumb length and not the length of side of the hopper. If you measured the side of the hopper, the plumb length is a bit less.
Edited 8/7/2007 9:42 pm ET by RedfordHenry
It's been a long, long time. . .Doesn't A^2+2AB+B^2 factor out to (A+B)^2?What A^2+AB+B^2 work out to?SamT
yes it does
19
I guess I wasn't very clear.What does A^2+AB+B^2 factor out to?I can add 4,6,and 9, without taking my socks off.SamT
Yeah, but they're those socks with toes, right?
So convenient a thing it is to be a reasonable Creature, since it enables one to find or make a Reason for everything one has a mind to do. --Benjamin Franklin
Who told you (|:>(SamT
Sam,
I don't think that the expression is going to "factor out" to anything recognizable or meaningful in the way you might expect.
If you're interested, here's a discussion of the development of the equation:
http://www.mathaware.org/mam/00/master/essays/dimension/dimen06.html
The expression for the volume of a rectangular pyramid is simply
V = (1/3) abh
where "a" and "b" are the dimensions of the base, and "h" the height.
Your pyramid would be 9 feet high if untruncated; total volume would be 27 cubic feet.
Looking at the "nose" alone, the base would be 2' x 2', with a height (nose only) of 6'; volume of the nose is therefore 8 cubic feet.
Therefore, the volume of your truncated pyramid is 27-8 = 19 cubic feet.
Are you talking about an insulation hopper?
Actually it is an excavation for a concrete base for an 18 ft steel pole. The base is 2x2x3D. Just trying to estimate the digging by hand. Means Construction data says 2 hrs. per yd in bad soil so im getting 1.4 hrs. With 20% fudge factor 1.7.
Oh OK, I understand now.
If it was an insulation hopper I was gonna say you wouldnt be able to fil it up to capacity anyway. At least none that I have come across yet anyway.
I didnt know you were estimating.