Thread: Help calculating the volume of a tray that is trapezoidal in both cross sections

1. Help calculating the volume of a tray that is trapezoidal in both cross sections

Hi there,
Although I used a lot of maths when I was at school and even doing quite well at it, it's been a while now and I am very rusty.

My company make a selection of slope sided food trays that are trapezoidal in both cross sections:

I would like to make an excel spreadsheet to calculate the volumes. Now when they are square this is not difficult as you can use the method of finding the volume of an incomplete pyramid, however I am having difficulty working out how to to this when they are rectangular in shape.

Thanks in advance for any help!

2. Re: Help calculating the volume of a tray that is trapezoidal in both cross sections

I've worked it out now thanks: one isosceles trapezoid prism, two triangular prisms and 4 pyramids.

3. Re: Help calculating the volume of a tray that is trapezoidal in both cross sections

a2
+---------------+
b2/ / \---------
+---------------+ \ |
/ | \ |
/................. |.... + | h
/ | / |
/ | / |
/ | /b1 ------
/ | /
/ | /
+-----------------------+
a1
Sorry I can not adjust figure
V = [a1*b1 + a2*b2 + (a1*b2 + a2*b1)/2] * h/3
using the average length and
width, is:

V = [a1*b1 + a2*b2 + 4((a1+a2)/2 * (b1+b2)/2)] * h/6
\___/ \___/ \___________________/
area of area of area of
bottom top middle
rectangle rectangle rectangle