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You might want to double check your calculation. You didn't give any numbers, but the spheres method that dmun described is more accurate and less susceptible to 'intuitive' errors.
If we ignore the vent (doorway) for the moment, it's easy to visualize that the dome is a sphere that is cut in half. So you can circumscribe half a sphere around the outside of the dome and another half sphere inside the dome. Then the entire space between the two half spheres would be filled by the dome. Ergo, subtracting the volume of the smaller dome from the larger will represent the dome wall volume.
Now contrast that against your method of calculating the area and multiplying by the thickness. Same thing, right? Well, no. If you were pouring a rectangular slab, it would be equivalent. But a dome has a curved surface. So say your dome will have an inside diameter of 100cm (radius = 50cm) & a wall thickness of 10cm. Did you use these numbers in your calculations? Or did you use the outside diameter (120cm) & radius (60cm)? Most people seem to opt for the former, but both approaches are wrong & give substantial errors of about 20%.
Since the dome wall thickness is not zero, as the diameter of the dome increases, so does the surface area. A reasonable approximation of the average dome surface area would be to take the diameter in the middle of the wall. In this case that would be 55cm. But the spheres method is still more accurate.
OOOOHHHH... the humanity, and the MATH.
LARS, my head hurts after reading your post...I didn't realize how stupid I have become. Literally took over 5 minutes to comprehend. I think you really do lose it if you don't use it (your mind)