How to get the right volume in a trapezoid box?

[natural sound]

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]

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

[xrk971]

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.

[picowallspeaker]

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

[Cal Weldon]

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]

Originally Posted by Cal Weldon

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]

Originally Posted by picowallspeaker

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]

Originally Posted by xrk971

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