Volume of Frustum Pyramid: 19800.44 ft^3Calculate Volume of Frustum Pyramid

[blimkie.k]

I had a similar question in the "engineering systems and design" category but didn't get any replies so hear is the simple version involving only the math.

Basically I just need to see if I am using the correct formula to the calculate the volume of a frustum pyramid. However the bottom of the pyramid is a 24"x24" square and the top would be a place which much much larger 6 sided shape, with all sides different lengths. I just need to know if this formula will work for a frustum pyramid with a square for one plane and a 6 sided shape for the other plane and a depth of 4" Here is my math.

This is not a school related question.

The formula was found on wikipedias entry for a frustum pyramid


Height = 4 inches Area 1 = 713392”
Area 2 = 756” (24”x24”)


Volume = (height *area1) – (height*area2)
3

= ( 4” * 713392”) -( 4” * 576”)
3

Volume = 2851264 inches cubed

Convert to feet cubed ( 1 ft^3 = 144 in^3

2851264 / 144 = 19800.44 feet cubed

 

[Xitami]

http://en.wikipedia.org/wiki/Frustum#Formulae"

$V=\frac{h}{3}\left(A_1+A_2+\sqrt{A_1A_2}\right)$
&
"[URL principle[/URL]

 

[blimkie.k]

Ok i see, I want to use that one because in my case the apex has allready been sliced off so I'm not finding the difference between a full pyramid and one with a flat top.

There was a mistake up there in my math the volume should actually be 950181.33 and the i pasted the formula in from word so it didn't show my underline which was intended to show division but anyways.


Also what is the difference between this and the heronian mean.

http://en.wikipedia.org/wiki/Heronian_mean

Running the formula this way gives me an even smaller number almost 4 times smaller.

 

[Xitami]

The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces.

$a_1=24^2, a_2=713392, h=4$

$V=\frac{h}{3}\left(A_1+A_2+\sqrt{A_1A_2}\right)$

$V\approx978985.345$

 

[CellCoree]

Yes, your calculation appears to be correct. The formula for calculating the volume of a frustum pyramid is V = (1/3)h(A1 + A2 + √(A1A2)), where h is the height, A1 and A2 are the areas of the two bases, and √ is the square root function. In your case, A1 is the area of the 6-sided top base and A2 is the area of the 24"x24" square base. As long as you have the correct measurements for the height and the two base areas, your calculation should be accurate.