# How to get the right volume in a trapezoid box?

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#### cross reference

Hello all ,

I have been working on a trapezoid design for 1 year now for my speakers and well it's not a new box desing to anyone it's my own design. Is there a easy way to figure out the volume for the inside of a trapezoid box? Here's a example. If the front and back of the box is 9 inch's on the bottom and 6 Inch's on top. Now for the the side's of the box. The bottom is 7 inche's on the bottom and 4 inch's on the top. So again how can I find the cubic feet inside this box? Well again thank you for all you help it's just I am new to this trapezoid box designing. Thanks Jm

#### Cal Weldon

Paid Member
Are these the inside dimensions? If not, give them, including the height.

#### xrk971

Paid Member
Depends of course on how tall the box is which you did not specify. I think the basic formula is very simple: take the average area of the top and bottom faces and multiply by the height. So it sounds like the base is 6in x 9in = 54in^2 and top is 4in x 7in = 28in^2. Average area is (54in^2+28in^2)/2=41in^2. Let's assume the height is 12in. So 41in^2 x 12in = 492 in^3.

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#### picowallspeaker

Just discompose the trapezoid in regular forms like parallelepipedes, triangular base prisms, cubes.

#### Cal Weldon

Paid Member
How the heck can we get so close but be different there X?
(6+9)/2=7.5
(4+7)/2=5.5

7.5x5.5x12=495 in^3
495/1728=0.286 ft^3

Based on ID of 12"

#### picowallspeaker

There's a fourth dimension...

#### xrk971

Paid Member
How the heck can we get so close but be different there X?
(6+9)/2=7.5
(4+7)/2=5.5

7.5x5.5x12=495 in^3
495/1728=0.286 ft^3

Based on ID of 12"

Why are you averaging the dimensions of each face? If you take the extreme example of a trapezoid that is straight like a regular rectangular box say 6x9x12, we would get doing it your way (6+9)/2=7.5 and 7.5x7.5x12= 675. Whereas the true vol is 54x12= 648.

I just think about it from a limits point of view as the area has to be the average between the two extremes of a rectangular box 6x9x12 and 4x7x12.

#### xrk971

Paid Member
Just discompose the trapezoid in regular forms like parallelepipedes, triangular base prisms, cubes.

gives same answer as mine but way more complicated.

#### picowallspeaker

Oh man! I never calculate anything! Just make a pipe well..er..about the longest in minimum space, make the section about speaker's diameter .... Put some Helmoltz resonators here and there, tar, bitumen, fluffy something .... #### Cal Weldon

Paid Member
Why are you averaging the dimensions of each face?
OK, let's do it a little different:

(6+9)/2=7.5X12=90 in^3 = area of one trapezoid
(4+7)/2=5.5X12=66 in^3 = area of the other trapezoid

90x66X144=855,360/1,728= 495in^3 or 0.286 ft^3

#### Cal Weldon

Paid Member
Why are you averaging the dimensions of each face?
Because the area of a trapezoid is
h(a+b)/2
where:
h=height
a=shorter of the parallel dimensions
b=longer of the parallels

Math

#### Cal Weldon

Paid Member
Sorry, I'm supposed to have forgotten all this by my age. #### Rullknufs

Shouldn't integrals work for this? Or am I wrong?

#### chrisb

for those with simple constant CSA just draw them out in CAD, and use the measure area function, snapping to intersection points, then times height

#### Cal Weldon

Paid Member
Ghosts of departed quantities. #### planet10

Paid Member
Cal & X fighting over the use of the Associative property.

dave

#### Cal Weldon

Paid Member
Cal & X fighting over the use of the Associative property.
Associative property, really?
take the average area of the top and bottom faces and multiply by the height. So it sounds like the base is 6in x 9in = 54in^2 and top is 4in x 7in = 28in^2.
Is that what you get from the dimensions in post 1?

#### Kindhornman

Has everyone actually forgotten there basic geometry? Cal, glad someones brain still works here and you go that right. Why would you have to use a cad program to figure this out? That is like asking what the area of a circle is! Now if we start talking about the sq. rt of -1 I imagine that many would not know the term i, but a simple trapezoid you could look that up on Google in two seconds. How do you do ac circuit work if you don't remember some basic math?

#### xrk971

Paid Member
Associative property, really?

Is that what you get from the dimensions in post 1?

I think we are on same thinking. Without a picture I interpreted trapezoid in the vertical dim with top wall and bottom wall being rectangular csa. I think you see this as a trapezoid csa on top and bottom wall of varying area - trapezoid in all dimensions. Not clear what op meant based on words. That's why we have diagrams. We are both right. Depends on interpretation. Heck op did not even give height. My formula of average areas on top and bottom multiplied by height applies to any cross section, round, trap, triangle, etc. As long as same type of cross section top and bottom.

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