# Volume of a trapezoidal shape

1. Oct 5, 2008

### drdizzard

Find the volume of the following figure, its just one part of a larger problem which is to find the center of gravity of a machine element. I know how to figure everything else out but I'm not sure how to find the volume of this shape so I can finish the problem

No equation was given to find the volume of the shape in the attachment, and its been way too long since I last took geometry.

I first tried to split it up into two seperate 3D shapes, the pyramid on top and the 3D rectangle on bottom and add the two volumes together but that didn't give me the right answer. I then tried to find the volume by calculating the area of the trapezoid and multiplying it by the width (2.7in) of the shape, that didn't work either.

2. Oct 5, 2008

### drdizzard

Here is a diagram of the shape. Forgot to attach it

3. Oct 5, 2008

### drdizzard

Sorry, had some difficulty getting this uploaded, but here is the shape

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4. Oct 6, 2008

### HallsofIvy

Staff Emeritus
Yes, the volume is the area of the trapezoid, 6(3+ 0.09)/2= 3(3.09)= 9.27 sq in, times the width: 9.27*2.7= 25.54 cubic inches. Since you don't say what you did or what you get I can't say where you went wrong.

As for finding the center of gravity, that's a much harder problem. One method would be to use integration. Another would be to "triangulate" the figure. That is, divide it into triangles (more correctly tetrahedrons- 3 dimensional figures with four vertices), average the vertices to find the center of gravity of each, then average those values, weighted by the volume of each.