Volume of a shape with a different trapezium at each end

1. Nov 26, 2009

oocon

1. Volume of a shape with a different trapezium at each end.
Trapezium 1: a(top side) = 65.5m, b = 35.5m, h = 3.5m, height above sea level = 3m. Trapezium 2: a = 53m, b = 17.5m, h = 3m, HASL = 1.6m. Trapezoids are parallel and 48m apart. Their horizontal centres are aligned (as in sections of a reservoir).

2. Need an equation

3. Need a solution!

2. Nov 26, 2009

LCKurtz

I assume the similar corners of the two trapezoids are connected by straight lines and you want the volume of the prism shaped solid that encloses. Consider a plane parallel to the ends at a distance x from one of the ends, giving a cross section area A(x). You should be able to figure the top, bottom and height of that cross section in terms of x using proportions. Once you have its area A(x) in terms of x, the volume would be

$$\int_0^{48} A(x)\,dx$$